# Playing Muller Games in a Hurry

John Fearnley and Martin Zimmermann

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.

First International Symposium on Games, Automata, Logic, and Formal Verification (GandALF 2010).

There is an extended journal version.