Abstract
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.
This work was partially supported by FWF NFN Grant S11407-N23 (RiSE) and a Microsoft faculty fellowship.
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Chatterjee, K., Doyen, L. (2011). Energy and Mean-Payoff Parity Markov Decision Processes. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_21
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