Supervisory control of a class of discrete event processes
SIAM Journal on Control and Optimization
On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
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
Games, Probability, and the Quantitative µ-Calculus qMµ
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
Information Processing Letters
Concurrent games with tail objectives
Theoretical Computer Science
Optimal strategy synthesis in stochastic Müller games
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Stochastic Müller games are PSPACE-complete
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Strategy improvement and randomized subexponential algorithms for stochastic parity games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
The complexity of stochastic rabin and streett games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Complexity bounds for regular games
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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The theory of graph games with @w-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 @w-regular winning conditions formalized as Muller winning conditions. We present optimal memory bounds for pure (deterministic) almost-sure winning and optimal winning strategies in stochastic graph games with Muller winning conditions. We also study the complexity of stochastic Muller games and show that both the qualitative and quantitative analysis problems are PSPACE-complete. Our results are relevant in synthesis of stochastic reactive processes.