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Complexity Theory (WS2019/20): Unterschied zwischen den Versionen

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David Carral (Diskussion | Beiträge)
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Stephan Mennicke (Diskussion | Beiträge)
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(68 dazwischenliegende Versionen von 4 Benutzern werden nicht angezeigt)
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|Tutors=David Carral
|Tutors=David Carral
|Term=WS
|Term=WS
|Year=2018
|Year=2019
|Lecture series=Complexity Theory
|Module=INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-TCSL, MCL-PI, MCL-KR,INF-E-3,INF-PM-FOR
|Module=INF-B-510, INF-B-520, INF-BAS6, INF-VERT6, MCL-TCSL, MCL-PI, MCL-KR,INF-E-3,INF-PM-FOR
|SWSLecture=4
|SWSLecture=4
Zeile 36: Zeile 37:
* The weekly exercise session will take place on Wednesdays DS3 (11.10 - 12.40).
* The weekly exercise session will take place on Wednesdays DS3 (11.10 - 12.40).
* Monday lecture sessions will take place in room APB/E008. All other lecture and exercise sessions will take place in room APB/E005.
* Monday lecture sessions will take place in room APB/E008. All other lecture and exercise sessions will take place in room APB/E005.
* '''Important:''' There will be neither lectures nor exercises on the first week of the semester. Therefore, the first lecture of this course will be on Monday, 15th of October.
* <b>Important:</b> as indicated in the class calendar below, the lecture sessions start on the 15th of October. Furthermore, there will be no exercise sessions on the 6th, 13th, and 20th of November.
|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 60: Zeile 61:
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Introduction
|Title=Introduction
|Room=APB E008
|Date=2018/10/15
|DS=DS2
|Download=CT2018-Lecture-01-overlay.pdf, CT2018-Lecture-01-print.pdf,
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=Turing Machines and Languages
|Room=APB E005
|Room=APB E005
|Date=2018/10/16
|Date=2019/10/15
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-02-overlay.pdf, CT2018-Lecture-02-print.pdf,
|Download=CT2019-Lecture-01-overlay.pdf,CT2019-Lecture-01-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 77: Zeile 70:
|Title=Mathematical Foundations, Decidability, and Recognisability
|Title=Mathematical Foundations, Decidability, and Recognisability
|Room=APB E005
|Room=APB E005
|Date=2018/10/17
|Date=2019/10/16
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-01-decidability-and-recognizability.pdf,
|Download=CT-WS2019-exercise-01.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Undecidability
|Title=Turing Machines and Languages
|Room=APB E008
|Room=APB E008
|Date=2018/10/22
|Date=2019/10/21
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-03-overlay.pdf,CT2018-Lecture-03-print.pdf,
|Download=CT2019-Lecture-02-overlay.pdf,CT2019-Lecture-02-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Undecidability and Recursion
|Title=Undecidability
|Room=APB E005
|Room=APB E005
|Date=2018/10/23
|Date=2019/10/22
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-04-overlay.pdf, CT2018-Lecture-04-print.pdf,
|Download=CT2019-Lecture-03-overlay.pdf,CT2019-Lecture-03-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 101: Zeile 94:
|Title=Undecidability and Rice's Theorem
|Title=Undecidability and Rice's Theorem
|Room=APB E005
|Room=APB E005
|Date=2018/10/24
|Date=2019/10/23
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-02.pdf,
|Download=CT-WS2019-exercise-02.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Time Complexity and Polynomial Time
|Title=Undecidability and Recursion
|Room=APB E008
|Room=APB E008
|Date=2018/10/29
|Date=2019/10/28
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-05-overlay.pdf, CT2018-Lecture-05-print.pdf,
|Download=CT2019-Lecture-04-overlay.pdf,CT2019-Lecture-04-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=NP
|Title=Time Complexity and Polynomial Time
|Room=APB E005
|Room=APB E005
|Date=2018/10/30
|Date=2019/10/29
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-06-overlay.pdf, CT2018-Lecture-06-print.pdf,
|Download=CT2019-Lecture-05-overlay.pdf,CT2019-Lecture-05-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Title=NP
|Room=APB E008
|Date=2019/10/30
|DS=DS3
|Download=CT2019-Lecture-06-overlay.pdf,CT2019-Lecture-06-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 125: Zeile 126:
|Title=NP-Completeness
|Title=NP-Completeness
|Room=APB E008
|Room=APB E008
|Date=2018/11/05
|Date=2019/11/04
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-07-overlay.pdf, CT2018-Lecture-07-print.pdf,
|Download=CT2019-Lecture-07-overlay.pdf,CT2019-Lecture-07-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 133: Zeile 134:
|Title=NP-Complete Problems
|Title=NP-Complete Problems
|Room=APB E005
|Room=APB E005
|Date=2018/11/06
|Date=2019/11/05
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-08-overlay.pdf, CT2018-Lecture-08-print.pdf
|Download=CT2019-Lecture-08-overlay.pdf,CT2019-Lecture-08-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Lehrveranstaltungstype=Übung
|Title=Time Complexity, PTime, and NP
|Title=Time Complexity, PTime, and NP
|Room=APB E005
|Room=APB E008
|Date=2018/11/07
|Date=2019/11/11
|DS=DS3
|DS=DS2
|Download=CT-WS2018-exercise-03.pdf,
|Download=CT-WS2019-exercise-03.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Space Complexity
|Title=Space Complexity
|Room=APB E008
|Room=APB E005
|Date=2018/11/12
|Date=2019/11/12
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-09-overlay.pdf, CT2018-Lecture-09-print.pdf,
|Download=CT2019-Lecture-09-overlay.pdf,CT2019-Lecture-09-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Polynomial Space
|Title=Polynomial Space
|Room=APB E005
|Room=APB E008
|Date=2018/11/13
|Date=2019/11/18
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-10-overlay.pdf,CT2018-Lecture-10-print.pdf,
|Download=CT2019-Lecture-10-overlay.pdf,CT2019-Lecture-10-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Lehrveranstaltungstype=Vorlesung
|Title=NP-Completeness and Time Complexity
|Title=Games/Logarithmic Space
|Room=APB E005
|Room=APB E005
|Date=2018/11/14
|Date=2019/11/19
|DS=DS3
|DS=DS2
|Download=CT-WS2018-exercise-04.pdf
|Download=CT2019-Lecture-11-overlay.pdf,CT2019-Lecture-11-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Games/Logarithmic Space
|Title=The Time Hierarchy Theorem
|Room=APB E008
|Room=APB E008
|Date=2018/11/19
|Date=2019/11/25
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-11-overlay.pdf, CT2018-Lecture-11-print.pdf,
|Download=CT2019-Lecture-12-overlay.pdf,CT2019-Lecture-12-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=The Time Hierarchy Theorem
|Title=Space Hierarchy and Gaps
|Room=APB E005
|Room=APB E005
|Date=2018/11/20
|Date=2019/11/26
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-12-overlay.pdf, CT2018-Lecture-12-print.pdf
|Download=CT2019-Lecture-13-overlay.pdf,CT2019-Lecture-13-print.pdf
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=NP-Completeness and Time Complexity
|Room=APB E005
|Date=2019/11/27
|DS=DS3
|Download=CT-WS2019-exercise-04-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Space Hierarchy and Gaps
|Title=P vs. NP: Ladner's Theorem
|Room=APB E008
|Room=APB E008
|Date=2018/11/26
|Date=2019/12/02
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-13-overlay.pdf, CT2018-Lecture-13-print.pdf,
|Download=CT2019-Lecture-14-overlay.pdf,CT2019-Lecture-14-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Space Hierarchy and Gaps (continued)
|Title=P vs. NP and Diagonalisation
|Room=APB E005
|Room=APB E005
|Date=2018/11/27
|Date=2019/12/03
|DS=DS2
|DS=DS2
|Download=CT2019-Lecture-15-overlay.pdf,CT2019-Lecture-15-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 204: Zeile 214:
|Title=Space Complexity
|Title=Space Complexity
|Room=APB E005
|Room=APB E005
|Date=2018/11/28
|Date=2019/12/04
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-05.pdf,
|Download=CT-WS2019-exercise-05.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=P vs. NP: Ladner's Theorem
|Title=Alternation
|Room=APB E008
|Room=APB E008
|Date=2018/12/03
|Date=2019/12/09
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-14-overlay.pdf, CT2018-Lecture-14-print.pdf,
|Download=CT2019-Lecture-16-overlay.pdf,CT2019-Lecture-16-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=P vs. NP and Diagonalisation
|Title=The Polynomial Hierarchy
|Room=APB E005
|Room=APB E005
|Date=2018/12/04
|Date=2019/12/10
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-15-overlay.pdf, CT2018-Lecture-15-print.pdf,
|Download=CT2019-Lecture-17-overlay.pdf,CT2019-Lecture-17-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 228: Zeile 238:
|Title=Diagonalisation
|Title=Diagonalisation
|Room=APB E005
|Room=APB E005
|Date=2018/12/05
|Date=2019/12/11
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-06.pdf,
|Download=CT-WS2019-exercise-06-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Alternation
|Title=Questions and Answers
|Room=APB E008
|Room=APB E008
|Date=2018/12/10
|Date=2019/12/16
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-16-overlay.pdf, CT2018-Lecture-16-print.pdf,
|Download=CT2019-Lecture-18-overlay.pdf,CT2019-Lecture-18-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Übung
|Title=The Polynomial Hierarchy
|Title=Diagonalisation and Alternation
|Room=APB E005
|Room=APB E005
|Date=2018/12/11
|Date=2019/12/17
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-17-overlay.pdf, CT2018-Lecture-17-print.pdf
|Download=CT-WS2019-exercise-07-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Lehrveranstaltungstype=Übung
|Title=Diagonalisation and Alternation
|Title=---
|Room=APB E005
|Room=APB E005
|Date=2018/12/12
|Date=2019/12/18
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-07.pdf,
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Polynomial Hierarchy / Circuit Complexity
|Title=Circuit Complexity
|Room=APB E008
|Room=APB E008
|Date=2018/12/17
|Date=2020/01/06
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-18-overlay.pdf, CT2018-Lecture-18-print.pdf,
|Download=CT2019-Lecture-19-overlay.pdf,CT2019-Lecture-19-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Questions and Answers
|Title=Circuits for Parallel Computation
|Room=APB E005
|Room=APB E005
|Date=2018/12/18
|Date=2020/01/07
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-19-overlay.pdf, CT2018-Lecture-19-print.pdf,
|Download=CT2019-Lecture-20-overlay.pdf,CT2019-Lecture-20-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 276: Zeile 285:
|Title=Alternation and the Polynomial Hierarchy
|Title=Alternation and the Polynomial Hierarchy
|Room=APB E005
|Room=APB E005
|Date=2018/12/19
|Date=2020/01/08
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-08.pdf,
|Download=CT-WS2019-exercise-08-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Circuits for Parallel Computation
|Title=Probabilistic Turing Machines
|Room=APB E008
|Room=APB E008
|Date=2019/01/07
|Date=2020/01/13
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-20-overlay.pdf, CT2018-Lecture-20-print.pdf,
|Download=CT2019-Lecture-21-overlay.pdf,CT2019-Lecture-21-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Turing Machines
|Title=Probabilistic Complexity Classes (1)
|Room=APB E005
|Room=APB E005
|Date=2019/01/08
|Date=2020/01/14
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-21-overlay.pdf, CT2018-Lecture-21-print.pdf,
|Download=CT2019-Lecture-22-overlay.pdf,CT2019-Lecture-22-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 300: Zeile 309:
|Title=Circuit Complexity
|Title=Circuit Complexity
|Room=APB E005
|Room=APB E005
|Date=2019/01/09
|Date=2020/01/15
|DS=DS3
|DS=DS3
|Download=Exercise-9-circuit-complexity.pdf,
|Download=CT-WS2019-exercise-09-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Complexity Classes (1)
|Title=Probabilistic Complexity Classes (2)
|Room=APB E008
|Room=APB E008
|Date=2019/01/14
|Date=2020/01/20
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-22-overlay.pdf, CT2018-Lecture-22-print.pdf,
|Download=CT2019-Lecture-23-overlay.pdf,CT2019-Lecture-23-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Complexity Classes (2)
|Title=Quantum Computing (1)
|Room=APB E005
|Room=APB E005
|Date=2019/01/15
|Date=2020/01/21
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-23-overlay.pdf, CT2018-Lecture-23-print.pdf,
|Download=CT2019-Lecture-24-overlay.pdf,CT2019-Lecture-24-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 324: Zeile 333:
|Title=Probabilistic TMs and ComplexityClasses
|Title=Probabilistic TMs and ComplexityClasses
|Room=APB E005
|Room=APB E005
|Date=2019/01/16
|Date=2020/01/22
|DS=DS3
|DS=DS3
|Download=CT-WS2018-exercise-10.pdf,
|Download=CT-WS2019-exercise-10-2.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Vorlesung
|Title=Quantum Computing (1)
|Title=Quantum Computing (2)
|Room=APB E008
|Room=APB E008
|Date=2019/01/21
|Date=2020/01/27
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-24-overlay.pdf, CT2018-Lecture-24-print.pdf,
|Download=CT2019-Lecture-25-overlay.pdf,CT2019-Lecture-25-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Vorlesung
|Lehrveranstaltungstype=Entfällt
|Title=Quantum Computing (2)
|Title=(no lecture)
|Room=APB E005
|Room=APB E005
|Date=2019/01/22
|Date=2020/01/28
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-25-overlay.pdf, CT2018-Lecture-25-print.pdf,
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Lehrveranstaltungstype=Vorlesung
|Title=Probabilistic Complexity Classes (3)
|Title=Interactive Proof Systems
|Room=APB E005
|Room=APB E005
|Date=2019/01/23
|Date=2020/02/03
|DS=DS3
|DS=DS2
|Download=CT-WS2018-exercise-11.pdf,
|Download=CT2019-Lecture-26-overlay.pdf,CT2019-Lecture-26-print.pdf
}}
}}
{{Vorlesung Zeiten
{{Vorlesung Zeiten
Zeile 356: Zeile 364:
|Title=Summary, Outlook, Consultation
|Title=Summary, Outlook, Consultation
|Room=APB E005
|Room=APB E005
|Date=2019/01/29
|Date=2020/02/04
|DS=DS2
|DS=DS2
|Download=CT2018-Lecture-26-overlay.pdf, CT2018-Lecture-26-print.pdf,
}}
{{Vorlesung Zeiten
|Lehrveranstaltungstype=Übung
|Title=Probabilistic Complexity Classes (3)
|Room=APB E005
|Date=2020/02/05
|DS=DS3
|Download=CT-WS2019-exercise-11-2.pdf
}}
}}

Aktuelle Version vom 11. Oktober 2021, 18:56 Uhr

Complexity Theory

Lehrveranstaltung mit SWS 4/2/0 (Vorlesung/Übung/Praktikum) in WS 2019

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 will be published on this page (see Dates & Materials above)

  • The weekly lecture sessions will take place on Mondays DS2 (9.20 - 10.50) and Tuesdays DS2 (9.20 - 10.50).
  • The weekly exercise session will take place on Wednesdays DS3 (11.10 - 12.40).
  • Monday lecture sessions will take place in room APB/E008. All other lecture and exercise sessions will take place in room APB/E005.
  • Important: as indicated in the class calendar below, the lecture sessions start on the 15th of October. Furthermore, there will be no exercise sessions on the 6th, 13th, and 20th of November.
  • 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 DS2, 15. Oktober 2019 in APB E005 Datei 1,  Datei 2
Übung Mathematical Foundations, Decidability, and Recognisability DS3, 16. Oktober 2019 in APB E005 Datei
Vorlesung Turing Machines and Languages DS2, 21. Oktober 2019 in APB E008 Datei 1,  Datei 2
Vorlesung Undecidability DS2, 22. Oktober 2019 in APB E005 Datei 1,  Datei 2
Übung Undecidability and Rice's Theorem DS3, 23. Oktober 2019 in APB E005 Datei
Vorlesung Undecidability and Recursion DS2, 28. Oktober 2019 in APB E008 Datei 1,  Datei 2
Vorlesung Time Complexity and Polynomial Time DS2, 29. Oktober 2019 in APB E005 Datei 1,  Datei 2
Vorlesung NP DS3, 30. Oktober 2019 in APB E008 Datei 1,  Datei 2
Vorlesung NP-Completeness DS2, 4. November 2019 in APB E008 Datei 1,  Datei 2
Vorlesung NP-Complete Problems DS2, 5. November 2019 in APB E005 Datei 1,  Datei 2
Übung Time Complexity, PTime, and NP DS2, 11. November 2019 in APB E008 Datei
Vorlesung Space Complexity DS2, 12. November 2019 in APB E005 Datei 1,  Datei 2
Vorlesung Polynomial Space DS2, 18. November 2019 in APB E008 Datei 1,  Datei 2
Vorlesung Games/Logarithmic Space DS2, 19. November 2019 in APB E005 Datei 1,  Datei 2
Vorlesung The Time Hierarchy Theorem DS2, 25. November 2019 in APB E008 Datei 1,  Datei 2
Vorlesung Space Hierarchy and Gaps DS2, 26. November 2019 in APB E005 Datei 1,  Datei 2
Übung NP-Completeness and Time Complexity DS3, 27. November 2019 in APB E005 Datei
Vorlesung P vs. NP: Ladner's Theorem DS2, 2. Dezember 2019 in APB E008 Datei 1,  Datei 2
Vorlesung P vs. NP and Diagonalisation DS2, 3. Dezember 2019 in APB E005 Datei 1,  Datei 2
Übung Space Complexity DS3, 4. Dezember 2019 in APB E005 Datei
Vorlesung Alternation DS2, 9. Dezember 2019 in APB E008 Datei 1,  Datei 2
Vorlesung The Polynomial Hierarchy DS2, 10. Dezember 2019 in APB E005 Datei 1,  Datei 2
Übung Diagonalisation DS3, 11. Dezember 2019 in APB E005 Datei
Vorlesung Questions and Answers DS2, 16. Dezember 2019 in APB E008 Datei 1,  Datei 2
Übung Diagonalisation and Alternation DS2, 17. Dezember 2019 in APB E005 Datei
Übung --- DS3, 18. Dezember 2019 in APB E005
Vorlesung Circuit Complexity DS2, 6. Januar 2020 in APB E008 Datei 1,  Datei 2
Vorlesung Circuits for Parallel Computation DS2, 7. Januar 2020 in APB E005 Datei 1,  Datei 2
Übung Alternation and the Polynomial Hierarchy DS3, 8. Januar 2020 in APB E005 Datei
Vorlesung Probabilistic Turing Machines DS2, 13. Januar 2020 in APB E008 Datei 1,  Datei 2
Vorlesung Probabilistic Complexity Classes (1) DS2, 14. Januar 2020 in APB E005 Datei 1,  Datei 2
Übung Circuit Complexity DS3, 15. Januar 2020 in APB E005 Datei
Vorlesung Probabilistic Complexity Classes (2) DS2, 20. Januar 2020 in APB E008 Datei 1,  Datei 2
Vorlesung Quantum Computing (1) DS2, 21. Januar 2020 in APB E005 Datei 1,  Datei 2
Übung Probabilistic TMs and ComplexityClasses DS3, 22. Januar 2020 in APB E005 Datei
Vorlesung Quantum Computing (2) DS2, 27. Januar 2020 in APB E008 Datei 1,  Datei 2
Entfällt (no lecture) DS2, 28. Januar 2020 in APB E005
Vorlesung Interactive Proof Systems DS2, 3. Februar 2020 in APB E005 Datei 1,  Datei 2
Vorlesung Summary, Outlook, Consultation DS2, 4. Februar 2020 in APB E005
Übung Probabilistic Complexity Classes (3) DS3, 5. Februar 2020 in APB E005 Datei


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