Perfect-Information Stochastic Mean-Payoff Parity Games
نویسندگان
چکیده
The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 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 212 -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 · 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 212 -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).
منابع مشابه
Blackwell Optimal Strategies in Priority mean-Payoff Games
One of the recurring themes in the theory of stochastic games is the interplay between discounted games and mean-payoff games. This culminates in the seminal paper of Mertens and Neyman [12] showing that mean-payoff games have a value and this value is the limit of the values of discounted games when the discount factor tends to 1. Note however that optimal strategies in both games are very dif...
متن کاملPerfect Information Stochastic Priority Games
We introduce stochastic priority games — a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination...
متن کاملThe Complexity of Solving Stochastic Games on Graphs
We consider some well-known families of two-player zero-sum perfect-information stochastic games played on finite directed graphs. Generalizing and unifying results of Liggett and Lippman, Zwick and Paterson, and Chatterjee and Henzinger, we show that the following tasks are polynomial-time (Turing) equivalent. – Solving stochastic parity games, – Solving simple stochastic games, – Solving stoc...
متن کاملReduction of stochastic parity to stochastic mean-payoff games
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 parity objectives, and mean-payoff (or limit-average) objectives. These games lie in NP ∩ coNP. We present a polynomial-time Turing reduction of stochastic parity games to stochastic mean-payoff games.
متن کاملStochastic Games with Parity Mean-payoff Objective
In this paper, we compute value of two-player games with perfect information equipped with the Par∧Avg>0 objectives. Moreover we show that even though the optimal strategies may require infinite memory, there exists an NP algorithm that computes the almost-sure region.
متن کامل