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Down the Borel Hierarchy: Solving Muller Games via Safety Games

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Executive Summary

The authors 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, they generalize their construction by presenting a new type of game reduction from infinite games to safety games and show its applicability to several other winning conditions.

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