  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.
