# Energy and mean-payoff parity Markov Decision Processes

Chatterjee K, Doyen L. 2011. Energy and mean-payoff parity Markov Decision Processes. MFCS: Mathematical Foundations of Computer Science, LNCS, vol. 6907, 206–218.

Conference Paper | Published | English

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Author
Chatterjee, KrishnenduISTA ; Doyen, Laurent
Department
Series Title
LNCS
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, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion 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, improving a recent PSPACE bound.
Publishing Year
Date Published
2011-09-28
Volume
6907
Page
206 - 218
Conference
MFCS: Mathematical Foundations of Computer Science
Conference Location
Warsaw, Poland
Conference Date
2011-08-22 – 2011-08-26
IST-REx-ID

### Cite this

Chatterjee K, Doyen L. Energy and mean-payoff parity Markov Decision Processes. In: Vol 6907. Springer; 2011:206-218. doi:10.1007/978-3-642-22993-0_21
Chatterjee, K., & Doyen, L. (2011). Energy and mean-payoff parity Markov Decision Processes (Vol. 6907, pp. 206–218). Presented at the MFCS: Mathematical Foundations of Computer Science, Warsaw, Poland: Springer. https://doi.org/10.1007/978-3-642-22993-0_21
Chatterjee, Krishnendu, and Laurent Doyen. “Energy and Mean-Payoff Parity Markov Decision Processes,” 6907:206–18. Springer, 2011. https://doi.org/10.1007/978-3-642-22993-0_21.
K. Chatterjee and L. Doyen, “Energy and mean-payoff parity Markov Decision Processes,” presented at the MFCS: Mathematical Foundations of Computer Science, Warsaw, Poland, 2011, vol. 6907, pp. 206–218.
Chatterjee K, Doyen L. 2011. Energy and mean-payoff parity Markov Decision Processes. MFCS: Mathematical Foundations of Computer Science, LNCS, vol. 6907, 206–218.
Chatterjee, Krishnendu, and Laurent Doyen. Energy and Mean-Payoff Parity Markov Decision Processes. Vol. 6907, Springer, 2011, pp. 206–18, doi:10.1007/978-3-642-22993-0_21.
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