Supervisory control of a class of discrete event processes
SIAM Journal on Control and Optimization
Markov decision processes and regular events
Proceedings of the seventeenth international colloquium on Automata, languages and programming
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
The complexity of stochastic games
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Competitive Markov decision processes
Competitive Markov decision processes
Languages, automata, and logic
Handbook of formal languages, vol. 3
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
How much memory is needed to win infinite games?
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Information Processing Letters
Optimal strategy synthesis in stochastic Müller games
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Strategy improvement and randomized subexponential algorithms for stochastic parity games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Complexity bounds for regular games
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Solving simple stochastic tail games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A survey of stochastic ω-regular games
Journal of Computer and System Sciences
The complexity of stochastic Müller games
Information and Computation
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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) fromeach state. We consider ω-regular winning conditions formalized as Müller winning conditions. We show that both the qualitative and quantitative problem for stochastic Müller games are PSPACE-complete.We also consider two well-known sub-classes of Müller objectives, namely, upwardclosed and union-closed objectives, and show that both the qualitative and quantitative problem for these sub-classes are coNP-complete.