Trading probability for Fairness

Marcin Jurdziński, Orna Kupferman, Thomas A. Henzinger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

Behavioral properties of open systems can be formalized as objectives in two-player games. Turn-based games model asynchronous interaction between the players (the system and its environment) by interleaving their moves. Concurrent games model synchronous interaction: the players always move simultaneously. Infinitary winning criteria are considered: Büchi, co-Büchi, and more general parity conditions. A generalization of determinacy for parity games to concurrent parity games demands probabilistic (mixed) strategies: either player 1 has a mixed strategy to win with probability 1 (almost-sure winning), or player 2 has a mixed strategy to win with positive probability. This work provides efficient reductions of concurrent probabilistic Büchi and co-Büchi games to turn-based games with Büchi condition and parity winning condition with three priorities, respectively. From a theoretical point of view, the latter reduction shows that one can trade the probabilistic nature of almost-sure winning for a more general parity (fairness) condition. The reductions improve understanding of concurrent games and provide an alternative simple proof of determinacy of concurrent Büchi and co-Büchi games. From a practical point of view, the reductions turn solvers of turn-based games into solvers of concurrent probabilistic games. Thus improvements in the well-studied algorithms for the former carry over immediately to the latter. In particular, a recent improvement in the complexity of solving turn-based parity games yields an improvement in time complexity of solving concurrent probabilistic co-Büchi games from cubic to quadratic.

Original languageAmerican English
Title of host publicationComputer Science Logic - 16th International Workshop, CSL 2002, 11th Annual Conference of the EACSL 2002, Proceedings
EditorsJulian Bradfield
PublisherSpringer Verlag
Pages292-305
Number of pages14
ISBN (Print)3540442405, 9783540442400
DOIs
StatePublished - 2002
Event16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002 - Edinburgh, United Kingdom
Duration: 22 Sep 200225 Sep 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2471
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Workshop on Computer Science Logic, CSL 2002 and 11th Annual Conference of the European Association for Computer Science Logic, EACSL 2002
Country/TerritoryUnited Kingdom
CityEdinburgh
Period22/09/0225/09/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

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