A direct symbolic algorithm for solving stochastic rabin games

We consider turn-based stochastic 2-player games on graphs with 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 with k pairs over a game graph with n vertices, our algorithm runs in 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 Fairsyn. We demonstrate the superiority of Fairsyn 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, Fairsyn performed significantly faster with up to two orders of magnitude improvement in computation time.