Abstract
The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use \(2\frac{1}{2}\)-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 \(2\frac{1}{2}\)-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·n 2d · 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 \(2\frac{1}{2}\)-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 Austrian Science Fund (FWF) Grant No P23499- N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), Microsoft Faculty Fellowship Award, and European project Cassting (FP7-601148).
Fuller version: IST Technical Report No IST-2013-128.
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Chatterjee, K., Doyen, L., Gimbert, H., Oualhadj, Y. (2014). Perfect-Information Stochastic Mean-Payoff Parity Games. In: Muscholl, A. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2014. Lecture Notes in Computer Science, vol 8412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54830-7_14
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