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Games and markov decision processes with mean-payoff parity and energy parity objectives
MEMICS'11 Proceedings of the 7th international conference on Mathematical and Engineering Methods in Computer Science
Playing games with counter automata
RP'12 Proceedings of the 6th international conference on Reachability Problems
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We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, while the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition requires that the resource level never drops below 0, and the mean-payoff condition requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean-payoff parity MDPs, the problem is solvable in polynomial time.