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Perfect-information stochastic mean-payoff parity games

K. Chatterjee, L. Doyen, H. Gimbert, Y. Oualhadj, Perfect-Information Stochastic Mean-Payoff Parity Games, IST Austria, 2013.

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Technical Report | Published | English
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IST Austria Technical Report
Abstract
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) with only parity objectives, or with only mean-payoff objectives. 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 2-1/2-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).
Publishing Year
Date Published
2013-07-08
Page
22
ISSN
IST-REx-ID

Cite this

Chatterjee K, Doyen L, Gimbert H, Oualhadj Y. Perfect-Information Stochastic Mean-Payoff Parity Games. IST Austria; 2013. doi:10.15479/AT:IST-2013-128-v1-1
Chatterjee, K., Doyen, L., Gimbert, H., & Oualhadj, Y. (2013). Perfect-information stochastic mean-payoff parity games. IST Austria. https://doi.org/10.15479/AT:IST-2013-128-v1-1
Chatterjee, Krishnendu, Laurent Doyen, Hugo Gimbert, and Youssouf Oualhadj. Perfect-Information Stochastic Mean-Payoff Parity Games. IST Austria, 2013. https://doi.org/10.15479/AT:IST-2013-128-v1-1.
K. Chatterjee, L. Doyen, H. Gimbert, and Y. Oualhadj, Perfect-information stochastic mean-payoff parity games. IST Austria, 2013.
Chatterjee K, Doyen L, Gimbert H, Oualhadj Y. 2013. Perfect-information stochastic mean-payoff parity games, IST Austria, 22p.
Chatterjee, Krishnendu, et al. Perfect-Information Stochastic Mean-Payoff Parity Games. IST Austria, 2013, doi:10.15479/AT:IST-2013-128-v1-1.
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