The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph games: the qualitative problem asks for the set of states from which a player can win with probability 1 (almost-sure winning); and the quantitative problem asks for the maximal probability of winning (optimal winning) from each state. We consider ω-regular winning conditions formalized as Müller winning conditions. We present optimal memory bounds for pure (deterministic) almost-sure winning and optimal winning strategies in stochastic graph games with Müller winning conditions. We also study the complexity of stochastic Müller games and show that both the qualitative and quantitative analysis problems are PSPACE-complete. Our results are relevant in synthesis of stochastic reactive processes.
Information and Computation
The research was supported by Austrian Science Fund (FWF) Grant No. P 23499-N23, FWF NFN Grant No. S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.
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Chatterjee K. The complexity of stochastic Müller games. Information and Computation. 2012;211:29-48. doi:10.1016/j.ic.2011.11.004
Chatterjee, K. (2012). The complexity of stochastic Müller games. Information and Computation, 211, 29–48. https://doi.org/10.1016/j.ic.2011.11.004
Chatterjee, Krishnendu. “The Complexity of Stochastic Müller Games.” Information and Computation 211 (2012): 29–48. https://doi.org/10.1016/j.ic.2011.11.004.
K. Chatterjee, “The complexity of stochastic Müller games,” Information and Computation, vol. 211, pp. 29–48, 2012.
Chatterjee K. 2012. The complexity of stochastic Müller games. Information and Computation. 211, 29–48.
Chatterjee, Krishnendu. “The Complexity of Stochastic Müller Games.” Information and Computation, vol. 211, Elsevier, 2012, pp. 29–48, doi:10.1016/j.ic.2011.11.004.
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