Chatterjee, KrishnenduIST Austria ; Doyen, Laurent; Gimbert, Hugo; Oualhadj, Youssouf
The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1/2-player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1/2-player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in time O(d·n2d·MeanGame) to compute the set of almost-sure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1/2-player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective).
This research was supported by European project Cassting (FP7-601148). A Technical Report of this paper is available at: https://repository.ist.ac.at/id/eprint/128.
210 - 225
FoSSaCS: Foundations of Software Science and Computation Structures
2014-04-05 – 2014-04-13
Chatterjee K, Doyen L, Gimbert H, Oualhadj Y. Perfect-information stochastic mean-payoff parity games. In: Vol 8412. Springer; 2014:210-225. doi:10.1007/978-3-642-54830-7_14
Chatterjee, K., Doyen, L., Gimbert, H., & Oualhadj, Y. (2014). Perfect-information stochastic mean-payoff parity games (Vol. 8412, pp. 210–225). Presented at the FoSSaCS: Foundations of Software Science and Computation Structures, Grenoble, France: Springer. https://doi.org/10.1007/978-3-642-54830-7_14
Chatterjee, Krishnendu, Laurent Doyen, Hugo Gimbert, and Youssouf Oualhadj. “Perfect-Information Stochastic Mean-Payoff Parity Games,” 8412:210–25. Springer, 2014. https://doi.org/10.1007/978-3-642-54830-7_14.
K. Chatterjee, L. Doyen, H. Gimbert, and Y. Oualhadj, “Perfect-information stochastic mean-payoff parity games,” presented at the FoSSaCS: Foundations of Software Science and Computation Structures, Grenoble, France, 2014, vol. 8412, pp. 210–225.
Chatterjee K, Doyen L, Gimbert H, Oualhadj Y. 2014. Perfect-information stochastic mean-payoff parity games. FoSSaCS: Foundations of Software Science and Computation Structures, LNCS, vol. 8412. 210–225.
Chatterjee, Krishnendu, et al. Perfect-Information Stochastic Mean-Payoff Parity Games. Vol. 8412, Springer, 2014, pp. 210–25, doi:10.1007/978-3-642-54830-7_14.
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