A Direct Symbolic Algorithm for Solving Stochastic Rabin Games

Tamajit Banerjee, Rupak Majumdar, Kaushik Mallik, Anne-Kathrin Schmuck, Sadegh Soudjani

Abstract: We consider turn-based stochastic 2-player games on graphs with \(\omega \)-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 \(O(n^{k+2}k!)\) symbolic steps, which improves the state of the art.