https://iccl.inf.tu-dresden.de/w/api.php?action=feedcontributions&user=David+Carral&feedformat=atomInternational Center for Computational Logic - Benutzerbeiträge [de]2024-03-28T12:57:05ZBenutzerbeiträgeMediaWiki 1.35.6https://iccl.inf.tu-dresden.de/w/index.php?title=Inproceedings3268&diff=32832Inproceedings32682021-02-14T17:24:59Z<p>David Carral: </p>
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<div>{{Publikation Erster Autor<br />
|ErsterAutorVorname=Efthymia<br />
|ErsterAutorNachname=Tsamoura<br />
|FurtherAuthors=David Carral; Enrico Malizia; Jacopo Urbani<br />
}}<br />
{{Inproceedings<br />
|Referiert=1<br />
|Title=Materializing Knowledge Bases via Trigger Graphs<br />
|To appear=1<br />
|Year=2021<br />
|Booktitle=Proceedings of the 47th International Conference on Very Large Databases, VLDB 2021<br />
|Publisher=Springer<br />
|Note=An extended version of this paper containing all formal arguments is available at https://arxiv.org/abs/2102.02753<br />
}}<br />
{{Publikation Details<br />
|Abstract=The chase is a well-established family of algorithms used to materialize Knowledge Bases (KBs) for tasks like query answering under dependencies or data cleaning. A general problem of chase algorithms is that they might perform redundant computations. To counter this problem, we introduce the notion of Trigger Graphs (TGs), which guide the execution of the rules avoiding redundant computations. We present the results of an extensive theoretical and empirical study that seeks to answer when and how TGs can be computed and what are the benefits of TGs when applied over real-world KBs. Our results include introducing algorithms that compute (minimal) TGs. We implemented our approach in a new engine, called GLog, and our experiments show that it can be significantly more efficient than the chase enabling us to materialize Knowledge Graphs with 17B facts in less than 40 min using a single machine with commodity hardware.<br />
|Download=Vldb-trigger-graphs.pdf<br />
|Projekt=CPEC, DIAMOND, ScaDS.AI<br />
|Forschungsgruppe=Wissensbasierte Systeme<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Inproceedings3268&diff=32831Inproceedings32682021-02-14T17:22:22Z<p>David Carral: </p>
<hr />
<div>{{Publikation Erster Autor<br />
|ErsterAutorVorname=Efthymia<br />
|ErsterAutorNachname=Tsamoura<br />
|FurtherAuthors=David Carral; Enrico Malizia; Jacopo Urbani<br />
}}<br />
{{Inproceedings<br />
|Referiert=1<br />
|Title=Materializing Knowledge Bases via Trigger Graphs<br />
|To appear=1<br />
|Year=2021<br />
|Booktitle=Proceedings of the 47th International Conference on Very Large Databases, VLDB 2021<br />
|Publisher=Springer-Verlag<br />
}}<br />
{{Publikation Details<br />
|Abstract=The chase is a well-established family of algorithms used to materialize Knowledge Bases (KBs) for tasks like query answering under dependencies or data cleaning. A general problem of chase algorithms is that they might perform redundant computations. To counter this problem, we introduce the notion of Trigger Graphs (TGs), which guide the execution of the rules avoiding redundant computations. We present the results of an extensive theoretical and empirical study that seeks to answer when and how TGs can be computed and what are the benefits of TGs when applied over real-world KBs. Our results include introducing algorithms that compute (minimal) TGs. We implemented our approach in a new engine, called GLog, and our experiments show that it can be significantly more efficient than the chase enabling us to materialize Knowledge Graphs with 17B facts in less than 40 min using a single machine with commodity hardware.<br />
|Download=Vldb-trigger-graphs.pdf<br />
|Projekt=CPEC, DIAMOND, ScaDS.AI<br />
|Forschungsgruppe=Wissensbasierte Systeme<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Inproceedings3268/en&diff=32830Inproceedings3268/en2021-02-14T17:21:12Z<p>David Carral: Page created automatically by parser function on page Inproceedings3268</p>
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<div>#REDIRECT [[Inproceedings3268]]</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Inproceedings3268&diff=32829Inproceedings32682021-02-14T17:21:12Z<p>David Carral: Die Seite wurde neu angelegt: „{{Publikation Erster Autor |ErsterAutorVorname=Efthymia |ErsterAutorNachname=Tsamoura |FurtherAuthors=David Carral; Enrico Malizia; Jacopo Urbani }} {{Inprocee…“</p>
<hr />
<div>{{Publikation Erster Autor<br />
|ErsterAutorVorname=Efthymia<br />
|ErsterAutorNachname=Tsamoura<br />
|FurtherAuthors=David Carral; Enrico Malizia; Jacopo Urbani<br />
}}<br />
{{Inproceedings<br />
|Referiert=1<br />
|Title=Materializing Knowledge Bases via Trigger Graphs<br />
|To appear=1<br />
|Year=2021<br />
|Booktitle=Proceedings of the 47th International Conference on Very Large Databases, VLDB 2021<br />
|Publisher=Springer-Verlag<br />
}}<br />
{{Publikation Details<br />
|Abstract=The chase is a well-established family of algorithms used to materialize Knowledge Bases (KBs) for tasks like query answering under dependencies or data cleaning. A general problem of chase algorithms is that they might perform redundant computations. To counter this problem, we introduce the notion of Trigger Graphs (TGs), which guide the execution of the rules avoiding redundant computations. We present the results of an extensive theoretical and empirical study that seeks to answer when and how TGs can be computed and what are the benefits of TGs when applied over real-world KBs. Our results include introducing algorithms that compute (minimal) TGs. We implemented our approach in a new engine, called GLog, and our experiments show that it can be significantly more efficient than the chase enabling us to materialize Knowledge Graphs with 17B facts in less than 40 min using a single machine with commodity hardware.<br />
|Download=Vldb-trigger-graphs.pdf<br />
|Projekt=DIAMOND<br />
|Forschungsgruppe=Wissensbasierte Systeme<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Vldb-trigger-graphs.pdf&diff=32828Datei:Vldb-trigger-graphs.pdf2021-02-14T17:20:58Z<p>David Carral: </p>
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<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32610Complexity Theory (WS2020)2021-02-01T12:22:26Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description====Important Announcement===<br />
<br />
If you want to contact David Carral, you may use his new [mailto:david.carral-martinez@inria.fr email address: david.carral-martinez@inria.fr]. His TUD email will not work after the 20th of January.<br />
<br />
===Exams===<br />
* All examinations will be oral remote exams.<br />
* The exams will on the 24th of February (Wednesday).<br />
* Students have to register for the exam by following the usual procedure for their study program and module. Once the examination date is known, students must contact the KBS secretary office (secretary_wbs@mailbox.tu-dresden.de) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4 SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6 SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6 SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book" (i.e., additional materials and lecture notes are not permitted).<br />
* The 15th Feb is the deadline for exam registration (i.e., the students must contact our secretary contacted our secretary with all the necessary forms to ask for a time slot by this date; it is NOT enough if only the examination office is informed on that day).<br />
<br />
===Content===<br />
* All examinations will be oral remote exams.<br />
* The exams will take place on the 24th of February<br />
* Students have to register for the exam by following the usual procedure for their study programme and module. Once the examination date is known, students must contact the KBS secretary office (<email>) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book", i.e., additional materials and lecture notes are not permitted.<br />
<br />
This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69260&p=4e19f26a<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69261&p=db6ac7f2<br />
|Date=2021/01/19<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-06.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf,Circuits-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69262&p=4fd000a5<br />
|Date=2021/01/26<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-07.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
|Download=Probabilistic-print.pdf,Probabilistic-slides.pdf,Probabilistic-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69263&p=f57a4b27<br />
|Date=2021/02/02<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-08.pdf<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Probabilistic-video.mkv&diff=32609Datei:Probabilistic-video.mkv2021-02-01T12:16:42Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Probabilistic-slides.pdf&diff=32608Datei:Probabilistic-slides.pdf2021-02-01T12:11:47Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Probabilistic-print.pdf&diff=32607Datei:Probabilistic-print.pdf2021-02-01T12:11:34Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32556Complexity Theory (WS2020)2021-01-22T12:43:07Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description====Important Announcement===<br />
<br />
If you want to contact David Carral, you may use his new [mailto:david.carral-martinez@inria.fr email address: david.carral-martinez@inria.fr]. His TUD email will not work after the 20th of January.<br />
<br />
===Exams===<br />
* All examinations will be oral remote exams.<br />
* The exams will on the 24th of February (Wednesday).<br />
* Students have to register for the exam by following the usual procedure for their study program and module. Once the examination date is known, students must contact the KBS secretary office (secretary_wbs@mailbox.tu-dresden.de) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4 SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6 SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6 SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book" (i.e., additional materials and lecture notes are not permitted).<br />
* The 15th Feb is the deadline for exam registration (i.e., the students must contact our secretary contacted our secretary with all the necessary forms to ask for a time slot by this date; it is NOT enough if only the examination office is informed on that day).<br />
<br />
===Content===<br />
* All examinations will be oral remote exams.<br />
* The exams will take place on the 24th of February<br />
* Students have to register for the exam by following the usual procedure for their study programme and module. Once the examination date is known, students must contact the KBS secretary office (<email>) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book", i.e., additional materials and lecture notes are not permitted.<br />
<br />
This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69260&p=4e19f26a<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69261&p=db6ac7f2<br />
|Date=2021/01/19<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-06.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf,Circuits-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69262&p=4fd000a5<br />
|Date=2021/01/26<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-07.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69263&p=f57a4b27<br />
|Date=2021/02/02<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Circuits-video.mkv&diff=32555Datei:Circuits-video.mkv2021-01-22T11:53:06Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32500Complexity Theory (WS2020)2021-01-14T18:02:06Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description====Important Announcement===<br />
<br />
If you want to contact David Carral, you may use his personal email: dcarralma@gmail.com. His TUD email will not work after the 20th of January.<br />
<br />
===Exams===<br />
* All examinations will be oral remote exams.<br />
* The exams will on the 24th of February (Wednesday).<br />
* Students have to register for the exam by following the usual procedure for their study program and module. Once the examination date is known, students must contact the KBS secretary office (secretary_wbs@mailbox.tu-dresden.de) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4 SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6 SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6 SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book" (i.e., additional materials and lecture notes are not permitted).<br />
* The 15th Feb is the deadline for exam registration (i.e., the students must contact our secretary contacted our secretary with all the necessary forms to ask for a time slot by this date; it is NOT enough if only the examination office is informed on that day).<br />
<br />
===Content===<br />
* All examinations will be oral remote exams.<br />
* The exams will take place on the 24th of February<br />
* Students have to register for the exam by following the usual procedure for their study programme and module. Once the examination date is known, students must contact the KBS secretary office (<email>) to submit the registration forms and to ask for a time slot.<br />
* The duration of exams for Foundations of Complexity Theory will correspond to 4SWS, unless another length is clearly stated in the email to the KBS secretary.<br />
* We also offer examinations for last year's Complexity Theory course (6SWS). Students who want to take this exam have to register for this course and should emphasize the length of 6SWS when asking for a time slot to avoid confusion.<br />
* Exams are "closed book", i.e., additional materials and lecture notes are not permitted.<br />
<br />
This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69260&p=4e19f26a<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69261&p=db6ac7f2<br />
|Date=2021/01/19<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69262&p=4fd000a5<br />
|Date=2021/01/26<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=https://selfservice.zih.tu-dresden.de/link.php?m=69263&p=f57a4b27<br />
|Date=2021/02/02<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32454Complexity Theory (WS2020)2021-01-07T19:51:53Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description====Important Announcement===<br />
<br />
If you want to contact David Carral, you may use his personal email: dcarralma@gmail.com. His TUD email will not work after the 20th of January.<br />
<br />
===Content===<br />
<br />
This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32453Complexity Theory (WS2020)2021-01-07T19:51:18Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description====Important Announcement===<br />
<br />
If you want to contact David Carral, you may use his personal email: dcarralma@gmail.com. My TUD email will not work after the 20th of January or so.<br />
<br />
===Content===<br />
<br />
This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32345Complexity Theory (WS2020)2021-01-04T11:58:03Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=Time-hierarchy-print.pdf,FCT-WS2020-Lecture-Video-10.mkv,Time-hierarchy-slides.pdf,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Time-hierarchy-slides.pdf&diff=32344Datei:Time-hierarchy-slides.pdf2021-01-04T11:57:59Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Time-hierarchy-print.pdf&diff=32343Datei:Time-hierarchy-print.pdf2021-01-04T11:57:42Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32342Complexity Theory (WS2020)2021-01-04T11:55:50Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-10-Print.pdf,FCT-WS2020-Lecture-Video-10.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32330Complexity Theory (WS2020)2021-01-01T17:13:39Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32329Complexity Theory (WS2020)2021-01-01T17:13:07Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
|Download=poly-hierarchy-print.pdf,Poly-hierarchy-slides.pdf,Poly-hierarchy-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
|Download=Circuits-print.pdf,Circuits-slides.pdf,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Circuits-slides.pdf&diff=32328Datei:Circuits-slides.pdf2021-01-01T17:12:55Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Circuits-print.pdf&diff=32327Datei:Circuits-print.pdf2021-01-01T17:12:31Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32326Complexity Theory (WS2020)2021-01-01T17:11:35Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
|Download=poly-hierarchy-print.pdf,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Poly-hierarchy-video.mkv&diff=32325Datei:Poly-hierarchy-video.mkv2021-01-01T17:05:10Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Poly-hierarchy-slides.pdf&diff=32324Datei:Poly-hierarchy-slides.pdf2021-01-01T17:03:00Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Poly-hierarchy-print.pdf&diff=32323Datei:Poly-hierarchy-print.pdf2021-01-01T17:02:50Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32322Complexity Theory (WS2020)2021-01-01T15:56:02Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
|Download=Alternation-print.pdf,Alternation-slides.pdf,Alternation-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Alternation-video.mkv&diff=32321Datei:Alternation-video.mkv2021-01-01T15:52:41Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Alternation-slides.pdf&diff=32320Datei:Alternation-slides.pdf2021-01-01T15:49:38Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Alternation-print.pdf&diff=32319Datei:Alternation-print.pdf2021-01-01T15:49:29Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32318Complexity Theory (WS2020)2020-12-31T18:59:30Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
|Download=Ladner-bgs-print.pdf,Ladner-bgs-slides.pdf,Ladner-bgs.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-bgs.mkv&diff=32317Datei:Ladner-bgs.mkv2020-12-31T18:56:29Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-bgs-slides.pdf&diff=32316Datei:Ladner-bgs-slides.pdf2020-12-31T18:53:09Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-bgs-print.pdf&diff=32315Datei:Ladner-bgs-print.pdf2020-12-31T18:52:54Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32314Complexity Theory (WS2020)2020-12-31T11:42:07Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
|Download=Ladner-print.pdf,Ladner-slides.pdf,Ladner-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-video.mkv&diff=32313Datei:Ladner-video.mkv2020-12-31T11:41:56Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-slides.pdf&diff=32312Datei:Ladner-slides.pdf2020-12-31T11:39:40Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Ladner-print.pdf&diff=32311Datei:Ladner-print.pdf2020-12-31T11:39:30Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32305Complexity Theory (WS2020)2020-12-30T11:07:00Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
|Download=Space-hierarchy-gap-print.pdf,Space-hierarchy-gap-slides.pdf,Space-hierarchy-gap-video.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Space-hierarchy-gap-video.mkv&diff=32304Datei:Space-hierarchy-gap-video.mkv2020-12-30T10:55:37Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Space-hierarchy-gap-slides.pdf&diff=32303Datei:Space-hierarchy-gap-slides.pdf2020-12-30T10:52:33Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:Space-hierarchy-gap-print.pdf&diff=32302Datei:Space-hierarchy-gap-print.pdf2020-12-30T10:52:23Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32301Complexity Theory (WS2020)2020-12-28T12:10:13Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,FCT-WS2020-Lecture-Video-10.mkv,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:FCT-WS2020-Lecture-Video-10.mkv&diff=32300Datei:FCT-WS2020-Lecture-Video-10.mkv2020-12-28T11:55:11Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Complexity_Theory_(WS2020)&diff=32248Complexity Theory (WS2020)2020-12-14T17:10:06Z<p>David Carral: </p>
<hr />
<div>{{Vorlesung<br />
|Title=Foundations of Complexity Theory<br />
|Research group=Wissensbasierte Systeme<br />
|Lecturers=David Carral<br />
|Tutors=Stephan Mennicke<br />
|Term=WS<br />
|Year=2020<br />
|Lecture series=Complexity Theory<br />
|Module=CMS-LM-MOC, CMS-LM-ADV, INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-KR, MCL-PI, MCL-TCSL<br />
|SWSLecture=2<br />
|SWSExercise=2<br />
|SWSPractical=0<br />
|Exam type=mündliche Prüfung<br />
|Description=This course covers the fundamental concepts as well as advanced topics of complexity theory.<br />
<br />
Key topics are:<br />
* '''Turing Machines (revision):''' Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration<br />
* '''Time Complexity:''' Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems<br />
* '''Space Complexity:''' Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL<br />
* '''Diagonalization:''' Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem<br />
* '''Alternation:''' Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--><br />
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)<br />
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem<br />
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results<br />
<br />
===Schedule and Location===<br />
<br />
Because of the ongoing COVID-19 pandemic, we are offering this lecture as an online course. Here are all the details:<br />
<ul><br />
<li> We will host the tutorials as "live sessions" on Tuesdays from 14:50 to 16:20. See the schedule of these sessions under the "Dates and Materials" tab for more information. </li><br />
<li> These "live sessions" will take place in a dedicated BigBlueButton room. To access this room, click on the Videokonferenz link associated with the tutorial session under "Dates and Materials". The room will be open 10 minutes before the beginning of each session. </li><br />
<li> Exercise sheets preparing for the tutorials and the final exams will be uploaded at least one week before the tutorial takes place. </li><br />
<li> Every week on Tuesday, we will publish either one video (if there is a tutorial happening on that week) or two videos (if there is none) with the weekly lectures. These videos will be posted on this webpage under the "Dates and Materials" tab. </li><br />
</ul><br />
<br />
===Legacy===<br />
<br />
Simliar courses have been taught at TU Dresden by Prof. Dr. [[Markus Krötzsch]] in previous years:<br />
<ul><br />
<li> [[Complexity_Theory_(WS2018)/en|Complexity Theory 2018]]<br />
<li> [[Complexity_Theory_(WS2019)|Complexity Theory 2019]]<br />
</ul><br />
Note that the lecture this year is a bit more compact than the ones offered in 2018 and 2019.<br />
<br />
===Acknowledgements===<br />
<br />
The slides for some of the foundational lectures of this course are based on slides used by Markus Krötzsch for the course ''Complexity Theory'' at the University of Oxford, which were adopted from slides created by [http://logic.las.tu-berlin.de/Members/Kreutzer/ Stefan Kreutzer] and [http://www.cs.ox.ac.uk/people/ian.horrocks/ Ian Horrocks] for that course. Further material has been prepared first by [[Daniel Borchmann/en|Daniel Borchmann]] during his time at TU Dresden.<br />
|Literature=* Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013<br />
:: Introductory text that covers all basic topics in this lecture.<br />
<br />
* Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en<br />
:: Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation<br />
<br />
* John E. Hopcroft and Jeffrey D. Ullman: ''Introduction to Automata Theory, Languages, and Computation''; Addison Wesley Publishing Company 1979<br />
:: The ''Cinderella Book''; contains a lot of information not contained in most other books; the hierarchy of undecidable problems as well as Rice' characterization of recognizable properties of recognizable languages are from here.<br />
<br />
* Christos H. Papadimitriou: ''Computational Complexity''; 1995 Addison-Wesley Publishing Company, Inc<br />
:: Standard reference text for many advanced aspects on complexity theory; the proofs of the Linear Speedup Theorem, the Gap Theorem, and Ladner's Theorem as given in the lecture are from here<br />
<br />
* Sanjeev Arora and Boaz Barak: ''Computational Complexity: A Modern Approach''; Cambridge University Press 2009<br />
:: Extensive book covering the state of the art of Complexity Theory<br />
<br />
* Michael R. Garey and David S. Johnson: ''Computers and Intractability''; Bell Telephone Laboratories, Inc. 1979<br />
:: The classical book on Complexity Theory; contains a long list of problems with their complexities<br />
<br />
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--><br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Introduction<br />
|Room=Screencast<br />
|Date=2020/10/27<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-01-Compressed.pdf,FCT-WS2020-Lecture-01.pdf,FCT-WS2020-Lecture-Video-01.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=Screencast<br />
|Date=2020/10/28<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-02-Compressed.pdf,FCT-WS2020-Lecture-02.pdf,FCT-WS2020-Lecture-Video-02.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Mathematical Foundations, Decidability, and Recognisability<br />
|Room=https://bigbluebutton.org/<br />
|Date=2020/11/03<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-01.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Time Complexity and Polynomial Time<br />
|Room=Screencast<br />
|Date=2020/11/04<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-03-compressed.pdf,FCT-WS2020-Lecture-03.pdf,FCT-WS2020-Lecture-Video-03.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP<br />
|Room=Screencast<br />
|Date=2020/11/10<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-04-Print.pdf,FCT-Lecture-04.pdf,FCT-WS2020-Lecture-Video-04.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Completeness<br />
|Room=Screencast<br />
|Date=2020/11/11<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-05-print.pdf,FCT-WS2020-Lecture-05.pdf,FCT-WS2020-Lecture-Video-05.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Time Complexity, PTime, and NP<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49420&p=36462527<br />
|Date=2020/11/17<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-02.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=NP-Complete Problems<br />
|Room=Screencast<br />
|Date=2020/11/18<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-06-Print.pdf,FCT-WS2020-Lecture-06.pdf,FCT-WS2020-Lecture-Video-06.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=NP-Completeness and Time Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=49425&p=dfc3e12e<br />
|Date=2020/11/24<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-03.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Complexity<br />
|Room=Screencast<br />
|Date=2020/11/25<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-07-Print.pdf,FCT-WS2020-Lecture-07.pdf,FCT-WS2020-Lecture-Video-07.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Polynomial Space<br />
|Room=Screencast<br />
|Date=2020/12/01<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-08-Print.pdf,FCT-WS2020-Lecture-08.pdf,FCT-WS2020-Lecture-Video-08.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Games/Logarithmic Space<br />
|Room=Screencast<br />
|Date=2020/12/02<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Print-09.pdf,FCT-WS2020-Lecture-Video-09.mkv<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Space Complexity<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54334&p=7b4aead4<br />
|Date=2020/12/08<br />
|DS=DS5<br />
|Download=FCT-WS2020-Exercise-04.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Time Hierarchy Theorem<br />
|Room=Screencast<br />
|Date=2020/12/09<br />
|DS=terminlos<br />
|Download=FCT-WS2020-Lecture-Video-11-Print.pdf,FCT-WS2020-Lecture-Video-11.pdf,<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Space Hierarchy and Gaps<br />
|Room=Screencast<br />
|Date=2020/12/15<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation<br />
|Room=https://selfservice.zih.tu-dresden.de/l/link.php?m=54335&p=81908897<br />
|Date=2020/12/15<br />
|DS=DS5<br />
|Download=CT-WS2020-Exercise-05.pdf<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP: Ladner's Theorem<br />
|Room=Screencast<br />
|Date=2021/01/05<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=P vs. NP and Diagonalisation<br />
|Room=Screencast<br />
|Date=2021/01/06<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Alternation<br />
|Room=Screencast<br />
|Date=2021/01/12<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Diagonalisation and Alternation<br />
|Room=BigBlueButton<br />
|Date=2021/01/12<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=The Polynomial Hierarchy<br />
|Room=Screencast<br />
|Date=2021/01/19<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Alternation and the Polynomial Hierarchy<br />
|Room=BigBlueButton<br />
|Date=2021/01/20<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Circuit Complexity<br />
|Room=Screencast<br />
|Date=2021/01/26<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Circuit Complexity<br />
|Room=BigBlueButton<br />
|Date=2021/01/27<br />
|DS=DS5<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Vorlesung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=Screencast<br />
|Date=2021/02/02<br />
|DS=terminlos<br />
}}<br />
{{Vorlesung Zeiten<br />
|Lehrveranstaltungstype=Übung<br />
|Title=Probabilistic Turing Machines and Complexity Classes<br />
|Room=BigBlueButton<br />
|Date=2021/02/03<br />
|DS=DS5<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:FCT-WS2020-Lecture-Video-11.pdf&diff=32247Datei:FCT-WS2020-Lecture-Video-11.pdf2020-12-14T17:10:02Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Datei:FCT-WS2020-Lecture-Video-11-Print.pdf&diff=32246Datei:FCT-WS2020-Lecture-Video-11-Print.pdf2020-12-14T17:09:33Z<p>David Carral: </p>
<hr />
<div></div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Article3062&diff=32115Article30622020-11-25T15:54:43Z<p>David Carral: </p>
<hr />
<div>{{Publikation Erster Autor<br />
|ErsterAutorVorname=David<br />
|ErsterAutorNachname=Carral<br />
|FurtherAuthors=Irina Dragoste; Markus Krötzsch<br />
}}<br />
{{Article<br />
|Referiert=1<br />
|Title=Reasoner = Logical Calculus + Rule Engine<br />
|To appear=0<br />
|Year=2020<br />
|Journal=KI<br />
|Publisher=Springer<br />
}}<br />
{{Publikation Details<br />
|Abstract=We propose using rule languages to encode complex reasoning algorithms in a declarative way. This approach -- which follows the classical slogan "Algorithm = Logic + Control" -- promises to turn high-level specifications of logical calculi as systems of inference rules into declarative rule-based models that can be executed on state-of-the-art rule engines.<br />
<br />
More precisely, given some input reasoning algorithm for some logic, we show how to produce a rule-based calculus; that is, a fixed rule set that can be used to replicate the consequences of the input algorithm. Simple rule languages suffice for simple logics, and we review our results on using Datalog rules to reason in the description logic EL. For more expressive logics, a suitably expressive yet implementable rule language often seems to be missing. To fill this gap, we consider an extension of Datalog with sets, Datalog(S), that can be executed by modern existential-rule reasoners, and we use it to present a rule-based reasoning calculus for the expressive description logic ALC.<br />
<br />
Because of some restrictions imposed by Springer, we cannot publish the manuscript on this page. To access the paper, click on the link below.<br />
|ISBN=1610-1987<br />
|Link=https://link.springer.com/article/10.1007/s13218-020-00667-6<br />
|DOI Name=10.1007/s13218-020-00667-6<br />
|Projekt=CPEC<br />
|Forschungsgruppe=Wissensbasierte Systeme<br />
}}</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Article3062/en&diff=32114Article3062/en2020-11-25T15:53:30Z<p>David Carral: Page created automatically by parser function on page Article3062</p>
<hr />
<div>#REDIRECT [[Article3062]]</div>David Carralhttps://iccl.inf.tu-dresden.de/w/index.php?title=Article3062&diff=32113Article30622020-11-25T15:53:30Z<p>David Carral: Die Seite wurde neu angelegt: „{{Publikation Erster Autor |ErsterAutorVorname=David |ErsterAutorNachname=Carral |FurtherAuthors=Irina Dragoste; Markus Krötzsch }} {{Article |Referiert=1 |Ti…“</p>
<hr />
<div>{{Publikation Erster Autor<br />
|ErsterAutorVorname=David<br />
|ErsterAutorNachname=Carral<br />
|FurtherAuthors=Irina Dragoste; Markus Krötzsch<br />
}}<br />
{{Article<br />
|Referiert=1<br />
|Title=Reasoner = Logical Calculus + Rule Engine<br />
|To appear=0<br />
|Year=2020<br />
|Journal=KI<br />
|Publisher=Springer<br />
}}<br />
{{Publikation Details<br />
|Abstract=We propose using rule languages to encode complex reasoning algorithms in a declarative way. This approach -- which follows the classical slogan "Algorithm = Logic + Control" -- promises to turn high-level specifications of logical calculi as systems of inference rules into declarative rule-based models that can be executed on state-of-the-art rule engines.<br />
<br />
More precisely, given some input reasoning algorithm for some logic, we show how to produce a rule-based calculus; that is, a fixed rule set that can be used to replicate the consequences of the input algorithm. Simple rule languages suffice for simple logics, and we review our results on using Datalog rules to reason in the description logic EL. For more expressive logics, a suitably expressive yet implementable rule language often seems to be missing. To fill this gap, we consider an extension of Datalog with sets, Datalog(S), that can be executed by modern existential-rule reasoners, and we use it to present a rule-based reasoning calculus for the expressive description logic ALC.<br />
|ISBN=1610-1987<br />
|Link=https://link.springer.com/article/10.1007/s13218-020-00667-6<br />
|DOI Name=10.1007/s13218-020-00667-6<br />
|Projekt=CPEC<br />
|Forschungsgruppe=Wissensbasierte Systeme<br />
}}</div>David Carral