Edit course information: Complexity Theory (WS2019/20)

Du bist aus dem folgenden Grund nicht berechtigt, diese Seite bearbeiten:

Diese Aktion ist auf Benutzer beschränkt, die der Gruppe „Benutzer“ angehören.

Course description

Title:	Complexity Theory Name of the lecture, in the language of the lecture
Research group:	Research groups offering this lecture; use Ctrl+click to select multiple groups
Lecturers:	List of lecturers, separated by semicolon
Tutors:	List of exercise tutors, separated by semicolon
Term:	Semester of this lecture; for winter semesters, the start year is used, e.g., WS 2014 for WS 2014/2015
Lecture series:	List of lecture series this lecture belongs to
Matrix channel:	Matrix channel associated with the course, e.g., `#example:example.org`
Modules:	Associated module ids, separated by commas
SWS:	// SWS for lectures/exercises/practicals
Type of examination:	Klausur mündliche Prüfung Hausarbeit Referat nach Modulbeschreibung Type(s) of examination; could be more than one; documentation of possible values
Description:	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 <!--; NTIME(n) ⊄ TISP(n¹·², n⁰·²)--> * '''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 [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 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. * <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. Description of topics and goals.
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. * Erich Grädel: ''Complexity Theory''; Lecture Notes, Winter Term 2009/10. Available online at https://logic.rwth-aachen.de/Teaching/KTQC-WS09/index.html.en :: 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 <!--* Neil Immerman: ''Descriptive Complexity''; Springer Verlag 1999--> Literature list (free text), use "*" at the start of lines to create bulleted lists

Dates of lectures and exercises

	Introduction
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Mathematical Foundations, Decidability, and Recognisability
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Turing Machines and Languages
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Undecidability
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Undecidability and Rice's Theorem
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Undecidability and Recursion
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Time Complexity and Polynomial Time
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	NP
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	NP-Completeness
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	NP-Complete Problems
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Time Complexity, PTime, and NP
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Space Complexity
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Polynomial Space
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Games/Logarithmic Space
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	The Time Hierarchy Theorem
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Space Hierarchy and Gaps
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	NP-Completeness and Time Complexity
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	P vs. NP: Ladner's Theorem
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	P vs. NP and Diagonalisation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Space Complexity
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Alternation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	The Polynomial Hierarchy
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Diagonalisation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Questions and Answers
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Diagonalisation and Alternation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	---
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Circuit Complexity
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Circuits for Parallel Computation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Alternation and the Polynomial Hierarchy
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Probabilistic Turing Machines
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Probabilistic Complexity Classes (1)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Circuit Complexity
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Probabilistic Complexity Classes (2)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Quantum Computing (1)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Probabilistic TMs and ComplexityClasses
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Quantum Computing (2)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	(no lecture)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Interactive Proof Systems
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Summary, Outlook, Consultation
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

	Probabilistic Complexity Classes (3)
Room:	Date and time: Room can also be an external link, which will display as “Video conference”; use “terminlos” as DS for sessions that don't have precise dates, e.g., multiple exercise sessions
Downloads:	Datei hochladen
Links to videos:	Links to (possibly external, e.g., YouTube-hosted) videos

Weitere hinzufügen

Zusammenfassung:

Abbrechen