Down the Borel Hierarchy: Solving Muller Games via Safety Games

Daniel Neider, Roman Rabinovich, Martin Zimmermann

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.

Third International Symposium on Games, Automata, Logic, and Formal Verification (GandALF 2012).

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