Vorlesung

Dozent: Prof. Dr. Volker Diekert, Armin Weiß

Termine

Zeit	Raum	Termine
Mo 17:30-19:00	V38.03
Di 11:30-13:00	0.108

Die Vorlesung findet als Präsenzveranstaltung statt. Beginn am 18.10.

Lernziele

Die Studierenden beherrschen typische Denk- und Herangehensweisen der Komplexitätstheorie. Dazu gehört insbesondere die Einordnung von Problemen in Komplexitätsklassen und die sich daraus ergebenden Konsequenzen für praktische Anwendungen (effizient lösbar/parallelisierbar etc.). Ferner kennen die Studierenden grundlegende Techniken zum Beweis unterer Schranken und wissen über die sich dabei ergebenden Schwierigkeiten Bescheid.

Inhalt

Die Komplexitätstheorie befasst sich mit der Klassifikation von Berechnungsproblemen nach ihrer Schwierigkeit (Komplexität), d.h. dem Bedarf an Ressourcen (Zeit, Speicher, etc.), um ein Problem auf einem bestimmten Maschinenmodell zu lösen. Diese Vorlesung baut auf den in “Theoretische Informatik 2” erworbenen Kenntnissen auf und vertieft diese. Insbesondere werden zahlreiche neue Komplexitätsklassen sowie parallele Berechnungsmodelle betrachtet und deren Relationen sowie typische Probleme untersucht. Ein Bestandteil ist hier auf der Beweis unterer Schranken. Typische Themen sind:

Komplexitätsklassen und vollständige Probleme:
- nichtdeterministische und alternierende Turingmaschinen, Polynomialzeithierarchie
- weitere NP-vollständige Probleme (z.B. Integer-Linear Programming)
Orakel-Turingmaschinen, “relative” Schwierigkeit von P=NP?
Dünne Mengen und der Satz von Mahaney
Interaktive Beweissysteme, Zero-Knowledge-Proofs
Schaltkreise als paralleles Berechnungsmodell:
- Parallele Algorithmen (Arithmetik, Erkennung kontextfreier Sprachen)
- Untere Schranken für monotone Schaltkreise
- Untere Schranken für Parity

Übungen

Finden ungefähr alle zwei Wochen statt. Genaue Termine werden noch bekannt gegeben.

Literatur

Uwe Schöning: Theoretische Informatik – kurzgefasst, 5. Auflage, Spektrum, 2008.
Volker Diekert: Komplexitätstheorie, Skript, Universität Stuttgart, 10.12.2007
Christos Papadimitriou: Computational Complexity, Addison Wesley, 30. November 1993
Heribert Vollmer: Introduction to Circuit Complexity, Springer, 1999
Sanjeev Arora, Boaz Barak: Computational Complexity: A Modern Approach, Cambridge University Press, 2009

News

[Jun’23] The paper “Parallel algorithms for power circuits and the word problem of the Baumslag group” by Caroline Mattes and Armin Weiß has been accepted at Computational Complexity.

[Oct’22] The paper “Lower Bounds for Sorting 16, 17, and 18 Elements” by Florian Stober and Armin Weiß has been accepted at ALENEX 2023.

[Sep’22] The paper “Conelikes and Ranker Comparisons” by Viktor Henriksson and Manfred Kufleitner has been accepted at LATIN 2022.

[Sep’22] The paper “Improved Parallel Algorithms for Generalized Baumslag Groups” by Caroline Mattes and Armin Weiß has been accepted at LATIN 2022.

[Apr’22] The paper “Reachability Games and Parity Games” by Volker Diekert and Manfred Kufleitner has been accepted at ICTAC 2022.

[Apr’22] The paper “Satisfiability Problems for Finite Groups” by Pawel M. Idziak, Piotr Kawalek, Jacek Krzaczkowski and Armin Weiß has been accepted at ICALP 2022.

All news

[Mar’22] The paper “The Power Word Problem in Graph Products” by Florian Stober and Armin Weiß was accepted at DLT 2022.

[Nov’20] Volker Diekert is Partner Investigator in the Australian ARC grant “Geodetic groups: foundational problems in algebra and computer science” at University of Technology Sydney.

[Apr’20] The paper “Groups with ALOGTIME-hard word problems and PSPACE-complete circuit value problems” by Laurent Bartholdi, Michael Figelius, Markus Lohrey and Armin Weiß has been accepted at CCC 2020.

[Apr’20] The paper “Hardness of equations over finite solvable groups under the exponential time hypothesis” by Armin Weiß has been accepted at ICALP 2020.

[Dec’19] The paper “An Automaton Group with PSPACE-Complete Word Problem” by Jan Philipp Wächter and Armin Weiß has been accepted at STACS 2020.

[Nov’19] Carlos Camino was awarded the stuvus Special Prize for exceptional commitment in teaching.

[Jun’19] The paper “The power word problem” by Markus Lohrey and Armin Weiß has been accepted at MFCS 2019.

[May’19] The paper “On the Average Case of MergeInsertion” by Florian Stober and Armin Weiß has been accepted at IWOCA 2019.

[Oct’18] The paper “Worst-Case Efficient Sorting with QuickMergesort” by Stefan Edelkamp and Armin Weiß has been accepted at ALENEX 2019.

[Jun’18] At CCC 2018, Lukas Fleischer received a Best Student Paper Award for his submission “On the Complexity of the Cayley Semigroup Membership Problem”.

[Jun’18] The paper “Testing Simon’s congruence” by Lukas Fleischer and Manfred Kufleitner was accepted at MFCS 2018.

[Jun’18] The paper “The Intersection Problem for Finite Semigroups” by Lukas Fleischer was accepted at DLT 2018.

[Apr’18] The paper “The isomorphism problem for finite extensions of free groups is in PSPACE” by Géraud Sénizergues and Armin Weiß was accepted at ICALP 2018.

[Apr’18] The paper “On the Complexity of the Cayley Semigroup Membership Problem” by Lukas Fleischer was accepted at CCC 2018.

[Jan’18] On March 24-29, 2019 Volker Diekert, Markus Lohrey, Olga Kharlampovich and Alexei Miasnikov will organize the Schloss Dagstuhl Seminar “Algorithmic Problems in Group Theory”.

[Dec’17] The paper “The Intersection Problem for Finite Monoids” by Lukas Fleischer and Manfred Kufleitner was accepted at STACS 2018.

[Jun’17] At the 12th International Computer Science Symposium in Russia (CSR), Lukas Fleischer and Manfred Kufleitner received a Best Paper Award for their publication “Green’s Relations in Finite Transformation Semigroups”, and Armin Weiss received a Best Paper Award for “The conjugacy problem in free solvable groups and wreath product of abelian groups is in $\text{TC}^0$ “ which is joint work with Alexei Miasnikov and Svetla Vassileva.