Simple Fixpoint Iteration To Solve Parity Games

Tom van Dijk, Bob Rubbens

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

1 Citation (Scopus)
13 Downloads (Pure)

Abstract

A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the many algorithms for parity games. We now consider a method of solving parity games by means of a naive fixpoint iteration. Several fixpoint algorithms for parity games have been proposed in the literature. In this work, we introduce an algorithm that relies on the notion of a distraction. The idea is that this offers a novel perspective for understanding parity games. We then show that this algorithm is in fact identical to two earlier published fixpoint algorithms for parity games and thus that these earlier algorithms are the same. Furthermore, we modify our algorithm to only partially recompute deeper fixpoints after updating a higher set and show that this modification enables a simple method to obtain winning strategies. We show that the resulting algorithm is simple to implement and offers good performance on practical parity games. We empirically demonstrate this using games derived from model-checking, equivalence checking and reactive synthesis and show that our fixpoint algorithm is the fastest solution for model-checking games.
Original languageEnglish
Title of host publicationProceedings Tenth International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2019
Subtitle of host publicationBordeaux, France, 2-3rd September 2019
EditorsJérôme Leroux, Jean-François Raskin
PublisherArXiv
Pages123-139
Number of pages17
DOIs
Publication statusPublished - 2019
Event10th International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2019 - Bordeaux, France
Duration: 2 Sep 20193 Sep 2019
Conference number: 10

Publication series

NameElectronic Proceedings in Theoretical Computer Science (EPTCS)
PublisherarXiv
Volume305
ISSN (Print)2075-2180

Conference

Conference10th International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2019
Abbreviated titleGandALF
CountryFrance
CityBordeaux
Period2/09/193/09/19

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