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Playing Muller Games in a Hurry

This work studies the following question: can plays in a Muller game be stopped after a finite number of moves and a winner be declared. A criterion to do this is sound if Player 0 wins an infinite-duration Muller game if and only if she wins the finite-duration version. A sound criterion is presented that stops a play after at most 3^n moves, where n is the size of the arena. This improves the bound (n!+1)^n obtained by McNaughton and the bound n!+1 derived from a reduction to parity games.