Energy and Mean-Payoff Parity Markov Decision Processes

  • Krishnendu Chatterjee
  • Laurent Doyen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)


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.


Polynomial Time Energy Parity Markov Decision Process Priority Function Parity Game 
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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Laurent Doyen
    • 2
  1. 1.IST Austria (Institute of Science and Technology Austria)Austria
  2. 2.LSV, ENS Cachan & CNRSFrance

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