Playing Muller Games in a Hurry

TL;DR

This paper introduces a sound criterion for stopping Muller games after a finite number of moves, ensuring correct winner determination, with a significantly improved bound of 3^n moves compared to previous bounds.

Contribution

It presents a new sound stopping criterion for Muller games that guarantees correct outcomes and improves the move bound from factorial-based estimates to exponential 3^n.

Findings

The criterion stops plays after at most 3^n moves.

It guarantees correctness: Player 0 wins infinite games iff she wins the finite version.

It improves previous bounds from factorial to exponential.

Abstract

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.