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
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
Weak alternating automata and tree automata emptiness
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A Discrete Subexponential Algorithm for Parity Games
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Faster Solutions of Rabin and Streett Games
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of 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
Games, Time, and Probability: Graph Models for System Design and Analysis
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice 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
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A stochastic graph game is played by two players on a game graph with probabilistic transitions. We consider stochastic graph games with ω-regular winning conditions specified as Rabin or Streett objectives. These games are NP-complete and coNP-complete, respectively. The value of the game for a player at a state s given an objective Φ is the maximal probability with which the player can guarantee the satisfaction of Φ from s. We present a strategy-improvement algorithm to compute values in stochastic Rabin games, where an improvement step involves solving Markov decision processes (MDPs) and nonstochastic Rabin games. The algorithm also computes values for stochastic Streett games but does not directly yield an optimal strategy for Streett objectives. We then show how to obtain an optimal strategy for Streett objectives by solving certain nonstochastic Streett games.