Down the Borel hierarchy: Solving Muller games via safety games

We transform a Muller game with n vertices into a safety game with (n!)3 vertices whose solution allows us to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel antichain-based memory structure, a compositional solution...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 560; pp. 219 - 234
Main Authors:	Neider, Daniel, Rabinovich, Roman, Zimmermann, Martin
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-12-2014
Subjects:	Algorithms Construction Game reductions Games Hierarchies Mathematical models Muller games Permissive strategies Safety Safety games Strategy Transforms Safety games Muller games Permissive strategies Game reductions
Online Access:	Get full text
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Summary:	We transform a Muller game with n vertices into a safety game with (n!)3 vertices whose solution allows us to determine the winning regions of the Muller game and to compute a finite-state winning strategy for one player. This yields a novel antichain-based memory structure, a compositional solution algorithm, and a natural notion of permissive strategies for Muller games. Moreover, we generalize our construction by presenting a new type of game reduction from infinite games to safety games and show its applicability to several other winning conditions.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2014.01.017