Algorithms for Büchi Games

Abstract

The classical algorithm for solving Büchi games requires time $O(n\cdot m)$ for game graphs with $n$ states and $m$ edges. For game graphs with constant outdegree, the best known algorithm has running time $O(n^2/\log n)$. We present two new algorithms for Büchi games. First, we give an algorithm that performs at most $O(m)$ more work than the classical algorithm, but runs in time O(n) on infinitely many graphs of constant outdegree on which the classical algorithm requires time $O(n^2)$. Second, we give an algorithm with running time $O(n\cdot m\cdot \log \delta (n)/\log n)$, where $1\le \delta (n)\le n$ is the outdegree of the game graph. Note that this algorithm performs asymptotically better than the classical algorithm if $\delta (n)=O(\log n)$.

11 Pages, Published in GDV 06 (Games in Design and Verification)