A Direct Symbolic Algorithm for Solving Stochastic Rabin Games

Abstract

Abstract We consider turn-based stochastic 2-player games on graphs with $$\omega $$ ω -regular winning conditions. We provide a direct symbolic algorithm for solving such games when the winning condition is formulated as a Rabin condition. For a stochastic Rabin game withkpairs over a game graph withnvertices, our algorithm runs in $$O(n^{k+2}k!)$$ O(nk+2k!) symbolic steps, which improves the state of the art. We have implemented our symbolic algorithm, along with performance optimizations including parallellization and acceleration, in a BDD-based synthesis tool called . We demonstrate the superiority of compared to the state of the art on a set of synthetic benchmarks derived from the VLTS benchmark suite and on a control system benchmark from the literature. In our experiments, performed significantly faster with up totwoorders of magnitude improvement in computation time.