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.
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.
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Banerjee, T., Majumdar, R., Mallik, K., Schmuck, AK., Soudjani, S. (2022). A Direct Symbolic Algorithm for Solving Stochastic Rabin Games. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13244. Springer, Cham. https://doi.org/10.1007/978-3-030-99527-0_5
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