Supervisory control of a class of discrete event processes
SIAM Journal on Control and Optimization
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
The complexity of stochastic games
Information and Computation
Languages, automata, and logic
Handbook of formal languages, vol. 3
Fixed point characterization of infinite behavior of finite-state systems
Theoretical Computer Science
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
Quantitative stochastic parity games
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Symbolic algorithms for verification and control
Symbolic algorithms for verification and control
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
The complexity of stochastic rabin and streett games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Stochastic Müller games are PSPACE-complete
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical 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) from each state. We consider ω-regular winning conditions formalized as Müller winning conditions. We present optimal memory bounds for pure almost-sure winning and optimal winning strategies in stochastic graph games with Müller winning conditions. We also present improved memory bounds for randomized almost-sure winning and optimal strategies.