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|Term=WS
|Term=WS
|Year=2017
|Year=2017
|Module=INF-BAS6, INF-VERT6, MCL-TCSL, MCL-PI, MCL-KR
|Lecture series=Complexity Theory
|Module=INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-TCSL, MCL-PI, MCL-KR
|SWSLecture=4
|SWSLecture=4
|SWSExercise=2
|SWSExercise=2
Zeile 22: Zeile 23:
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)
* '''Circuit Complexity:''' Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem
* '''Probabilistic Computation:''' Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem
* '''Quantum Computing:''' Quantum circuits, BQP, some basic results


===Legacy===
===Acknowledgements===


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.
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.
===Schedule and Location===
All dates are published on this page (see ''Dates & Materials'' above)
* The weekly lecture sessions will take place on Tuesdays DS3 (11:10 to 12:40), and Wednesdays DS6 (16:40 to 18:10).
* The weekly exercise session will take place on Tuesdays DS5 (14:50 to 16:20).
::The first exercise will take place in the second week, i.e., on 17 Oct 2017
* All sessions will take place in room APB/E005.
* '''Important:''' There will be no lectures or exercises in the third week (24th and 25th Oct 2017)
|Literature=* '''Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013'''
|Literature=* '''Michael Sipser: ''Introduction to the Theory of Computation, International Edition''; 3rd Edition; Cengage Learning 2013'''
:: Introductory text that covers all basic topics in this lecture.
:: Introductory text that covers all basic topics in this lecture.
Zeile 45: Zeile 58:


<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999-->
<!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999-->
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Introduction
|Room=APB E005
|Date=2017/10/10
|DS=DS3
|Download=CT2017-Lecture-01-overlay.pdf,CT2017-Lecture-01-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Turing Machines and Languages
|Room=APB E005
|Date=2017/10/11
|DS=DS6
|Download=CT2017-Lecture-02-overlay.pdf,CT2017-Lecture-02-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Undecidability
|Room=APB E005
|Date=2017/10/17
|DS=DS3
|Download=CT2017-Lecture-03-overlay.pdf,CT2017-Lecture-03-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Mathematical Foundations, Decidability, and Recognisability
|Room=APB E005
|Date=2017/10/17
|DS=DS5
|Download=CT2017-Exercise-01.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Undecidability and Recursion
|Room=APB E005
|Date=2017/10/18
|DS=DS6
|Download=CT2017-Lecture-04-overlay.pdf,CT2017-Lecture-04-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Time Complexity and Polynomial Time
|Room=APB E005
|Date=2017/11/01
|DS=DS6
|Download=CT2017-Lecture-05-overlay.pdf,CT2017-Lecture-05-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=NP
|Room=APB E005
|Date=2017/11/07
|DS=DS3
|Download=CT2017-Lecture-06-overlay.pdf,CT2017-Lecture-06-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Undecidability and Rice's Theorem
|Room=APB E005
|Date=2017/11/07
|DS=DS5
|Download=CT2017-Exercise-02.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=NP-Completeness
|Room=APB E005
|Date=2017/11/08
|DS=DS6
|Download=CT2017-Lecture-07-overlay.pdf,CT2017-Lecture-07-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=NP-Complete Problems
|Room=APB E005
|Date=2017/11/14
|DS=DS3
|Download=CT2017-Lecture-08-overlay.pdf,CT2017-Lecture-08-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Time Complexity, PTime, and NP
|Room=APB E005
|Date=2017/11/14
|DS=DS5
|Download=CT2017-Exercise-03.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Space Complexity
|Room=APB E005
|Date=2017/11/15
|DS=DS6
|Download=CT2017-Lecture-09-overlay.pdf,CT2017-Lecture-09-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Polynomial Space
|Room=APB E005
|Date=2017/11/21
|DS=DS3
|Download=CT2017-Lecture-10-overlay.pdf,CT2017-Lecture-10-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=NP-Completeness and Time Complexity
|Room=APB E005
|Date=2017/11/21
|DS=DS5
|Download=CT2017-Exercise-04.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Games/Logarithmic Space
|Room=APB E005
|Date=2017/11/28
|DS=DS3
|Download=CT2017-Lecture-11-overlay.pdf,CT2017-Lecture-11-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Space Complexity
|Room=APB E005
|Date=2017/11/28
|DS=DS5
|Download=CT2017-Exercise-05.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=The Time Hierarchy Theorem
|Room=APB E005
|Date=2017/11/29
|DS=DS6
|Download=CT2017-Lecture-12-overlay.pdf,CT2017-Lecture-12-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Space Hierarchy and Gaps
|Room=APB E005
|Date=2017/12/05
|DS=DS3
|Download=CT2017-Lecture-13-overlay.pdf,CT2017-Lecture-13-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Log-space Complexity and Diagonalization
|Room=APB E005
|Date=2017/12/05
|DS=DS5
|Download=CT2017-Exercise-06.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=P vs. NP: Ladner's Theorem
|Room=APB E005
|Date=2017/12/06
|DS=DS6
|Download=CT2017-Lecture-14-overlay.pdf,CT2017-Lecture-14-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=P vs. NP and Diagonalisation
|Room=APB E005
|Date=2017/12/12
|DS=DS3
|Download=CT2017-Lecture-15-overlay.pdf,CT2017-Lecture-15-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Diagonalisation
|Room=APB E005
|Date=2017/12/12
|DS=DS5
|Download=CT2017-Exercise-07.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Alternation
|Room=APB E005
|Date=2017/12/13
|DS=DS6
|Download=CT2017-Lecture-16-overlay.pdf,CT2017-Lecture-16-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=The Polynomial Hierarchy
|Room=APB E005
|Date=2017/12/19
|DS=DS3
|Download=CT2017-Lecture-17-overlay.pdf,CT2017-Lecture-17-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Diagonalisation and Alternation
|Room=APB E005
|Date=2017/12/19
|DS=DS5
|Download=CT2017-Exercise-08.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Questions and Answers
|Room=APB E005
|Date=2017/12/20
|DS=DS6
|Download=CT2017-Lecture-18-overlay.pdf,CT2017-Lecture-18-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Circuit Complexity
|Room=APB E005
|Date=2018/01/09
|DS=DS3
|Download=CT2017-Lecture-19-overlay.pdf,CT2017-Lecture-19-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Alternation and the Polynomial Hierarchy
|Room=APB E005
|Date=2018/01/09
|DS=DS5
|Download=CT2017-Exercise-09.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Circuits for Parallel Computation
|Room=APB E005
|Date=2018/01/10
|DS=DS6
|Download=CT2017-Lecture-20-overlay.pdf,CT2017-Lecture-20-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Turing Machines
|Room=APB E005
|Date=2018/01/16
|DS=DS3
|Download=CT2017-Lecture-21-overlay.pdf,CT2017-Lecture-21-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Circuit Complexity
|Room=APB E005
|Date=2018/01/16
|DS=DS5
|Download=CT2017-Exercise-10.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Complexity Classes (1)
|Room=APB E005
|Date=2018/01/17
|DS=DS6
|Download=CT2017-Lecture-22-overlay.pdf,CT2017-Lecture-22-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Complexity Classes (2)
|Room=APB E005
|Date=2018/01/23
|DS=DS3
|Download=CT2017-Lecture-23-overlay.pdf,CT2017-Lecture-23-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Probabilistic TMs and ComplexityClasses
|Room=APB E005
|Date=2018/01/23
|DS=DS5
|Download=CT2017-Exercise-11.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Quantum Computing (1)
|Room=APB E005
|Date=2018/01/24
|DS=DS6
|Download=CT2017-Lecture-24-overlay.pdf,CT2017-Lecture-24-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Quantum Computing (2)
|Room=APB E005
|Date=2018/01/30
|DS=DS3
|Download=CT2017-Lecture-25-overlay.pdf,CT2017-Lecture-25-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Probabilistic Complexity Classes (3)
|Room=APB E005
|Date=2018/01/30
|DS=DS5
|Download=CT2017-Exercise-13.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Summary, Outlook, Consultation
|Room=APB E005
|Date=2018/01/31
|DS=DS6
}}
}}

Aktuelle Version vom 26. Oktober 2020, 18:52 Uhr

Complexity Theory

Lehrveranstaltung mit SWS 4/2/0 (Vorlesung/Übung/Praktikum) in WS 2017

Dozent

Tutor

Umfang (SWS)

  • 4/2/0

Module

Leistungskontrolle

  • Mündliche Prüfung

Vorlesungsreihe


This course covers the fundamental concepts as well as advanced topics of complexity theory.

Key topics are:

  • Turing Machines (revision): Definition of Turing Machines; Variants; Computational Equivalence; Decidability and Recognizability; Enumeration
  • Undecidability: Examples of Undecidable Problems; Mapping Reductions; Rice’s Theorem (both for characterizing Decidability and Recognizability); Recursion Theorem; Outlook into Decidability in Logic
  • Time Complexity: Measuring Time Complexity; Many-One Reductions; Cook-Levin Theorem; Time Complexity Classes (P, NP, ExpTime); NP-completeness; pseudo-NP-complete problems
  • Space Complexity: Space Complexity Classes (PSpace, L, NL); Savitch’s Theorem; PSpace-completeness; NL-completeness; NL = coNL
  • Diagonalization: Hierarchy Theorems (det. Time, non-det. Time, Space); Gap Theorem; Ladner’s Theorem; Relativization; Baker-Gill-Solovay Theorem
  • Alternation: Alternating Turing Machines; APTime = PSpace; APSpace = ExpTime; Polynomial Hierarchy
  • Circuit Complexity: Boolean Circuits; Alternative Proof of Cook-Levin Theorem; Parallel Computation (NC); P-completeness; P/poly; (Karp-Lipton Theorem, Meyer’s Theorem)
  • Probabilistic Computation: Randomized Complexity Classes (RP, PP, BPP, ZPP); Sipser-Gács-Lautemann Theorem
  • Quantum Computing: Quantum circuits, BQP, some basic results

Acknowledgements

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 Stefan Kreutzer and Ian Horrocks for that course.

Further material has been prepared first by Daniel Borchmann during his time at TU Dresden.

Schedule and Location

All dates are published on this page (see Dates & Materials above)

  • The weekly lecture sessions will take place on Tuesdays DS3 (11:10 to 12:40), and Wednesdays DS6 (16:40 to 18:10).
  • The weekly exercise session will take place on Tuesdays DS5 (14:50 to 16:20).
The first exercise will take place in the second week, i.e., on 17 Oct 2017
  • All sessions will take place in room APB/E005.
  • Important: There will be no lectures or exercises in the third week (24th and 25th Oct 2017)
  • Michael Sipser: Introduction to the Theory of Computation, International Edition; 3rd Edition; Cengage Learning 2013
Introductory text that covers all basic topics in this lecture.
Free lecture notes with general overview of main results; more detailed than Sipser on oracles and alternation; main reference for randomized computation
  • John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation; Addison Wesley Publishing Company 1979
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.
  • Christos H. Papadimitriou: Computational Complexity; 1995 Addison-Wesley Publishing Company, Inc
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
  • Sanjeev Arora and Boaz Barak: Computational Complexity: A Modern Approach; Cambridge University Press 2009
Extensive book covering the state of the art of Complexity Theory
  • Michael R. Garey and David S. Johnson: Computers and Intractability; Bell Telephone Laboratories, Inc. 1979
The classical book on Complexity Theory; contains a long list of problems with their complexities

Veranstaltungskalender abonnieren (icalendar)

Vorlesung Introduction DS3, 10. Oktober 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Turing Machines and Languages DS6, 11. Oktober 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Undecidability DS3, 17. Oktober 2017 in APB E005 Datei 1,  Datei 2
Übung Mathematical Foundations, Decidability, and Recognisability DS5, 17. Oktober 2017 in APB E005 Datei
Vorlesung Undecidability and Recursion DS6, 18. Oktober 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Time Complexity and Polynomial Time DS6, 1. November 2017 in APB E005 Datei 1,  Datei 2
Vorlesung NP DS3, 7. November 2017 in APB E005 Datei 1,  Datei 2
Übung Undecidability and Rice's Theorem DS5, 7. November 2017 in APB E005 Datei
Vorlesung NP-Completeness DS6, 8. November 2017 in APB E005 Datei 1,  Datei 2
Vorlesung NP-Complete Problems DS3, 14. November 2017 in APB E005 Datei 1,  Datei 2
Übung Time Complexity, PTime, and NP DS5, 14. November 2017 in APB E005 Datei
Vorlesung Space Complexity DS6, 15. November 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Polynomial Space DS3, 21. November 2017 in APB E005 Datei 1,  Datei 2
Übung NP-Completeness and Time Complexity DS5, 21. November 2017 in APB E005 Datei
Vorlesung Games/Logarithmic Space DS3, 28. November 2017 in APB E005 Datei 1,  Datei 2
Übung Space Complexity DS5, 28. November 2017 in APB E005 Datei
Vorlesung The Time Hierarchy Theorem DS6, 29. November 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Space Hierarchy and Gaps DS3, 5. Dezember 2017 in APB E005 Datei 1,  Datei 2
Übung Log-space Complexity and Diagonalization DS5, 5. Dezember 2017 in APB E005 Datei
Vorlesung P vs. NP: Ladner's Theorem DS6, 6. Dezember 2017 in APB E005 Datei 1,  Datei 2
Vorlesung P vs. NP and Diagonalisation DS3, 12. Dezember 2017 in APB E005 Datei 1,  Datei 2
Übung Diagonalisation DS5, 12. Dezember 2017 in APB E005 Datei
Vorlesung Alternation DS6, 13. Dezember 2017 in APB E005 Datei 1,  Datei 2
Vorlesung The Polynomial Hierarchy DS3, 19. Dezember 2017 in APB E005 Datei 1,  Datei 2
Übung Diagonalisation and Alternation DS5, 19. Dezember 2017 in APB E005 Datei
Vorlesung Questions and Answers DS6, 20. Dezember 2017 in APB E005 Datei 1,  Datei 2
Vorlesung Circuit Complexity DS3, 9. Januar 2018 in APB E005 Datei 1,  Datei 2
Übung Alternation and the Polynomial Hierarchy DS5, 9. Januar 2018 in APB E005 Datei
Vorlesung Circuits for Parallel Computation DS6, 10. Januar 2018 in APB E005 Datei 1,  Datei 2
Vorlesung Probabilistic Turing Machines DS3, 16. Januar 2018 in APB E005 Datei 1,  Datei 2
Übung Circuit Complexity DS5, 16. Januar 2018 in APB E005 Datei
Vorlesung Probabilistic Complexity Classes (1) DS6, 17. Januar 2018 in APB E005 Datei 1,  Datei 2
Vorlesung Probabilistic Complexity Classes (2) DS3, 23. Januar 2018 in APB E005 Datei 1,  Datei 2
Übung Probabilistic TMs and ComplexityClasses DS5, 23. Januar 2018 in APB E005 Datei
Vorlesung Quantum Computing (1) DS6, 24. Januar 2018 in APB E005 Datei 1,  Datei 2
Vorlesung Quantum Computing (2) DS3, 30. Januar 2018 in APB E005 Datei 1,  Datei 2
Übung Probabilistic Complexity Classes (3) DS5, 30. Januar 2018 in APB E005 Datei
Vorlesung Summary, Outlook, Consultation DS6, 31. Januar 2018 in APB E005


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