Down the Borel Hierarchy: Solving Muller Games via Safety Games

Daniel Neider
(RWTH Aachen University)
Roman Rabinovich
(RWTH Aachen University)
Martin Zimmermann
(RWTH Aachen University and University of Warsaw)

We transform a Muller game with n vertices into a safety game with (n!)^3 vertices whose solution allows 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 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.

In Marco Faella and Aniello Murano: Proceedings Third International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2012), Napoli, Italy, September 6-8, 2012, Electronic Proceedings in Theoretical Computer Science 96, pp. 169–182.
Published: 7th October 2012.

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