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Qualitative Analysis of Partially-Observable Markov Decision Processes

  • Krishnendu Chatterjee
  • Laurent Doyen
  • Thomas A. Henzinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)

Abstract

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with parity objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider qualitative analysis problems: given a POMDP with a parity objective, decide whether there exists an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Büchi, and coBüchi objectives. We establish several upper and lower bounds that were not known in the literature. Second, we give optimal bounds (matching upper and lower bounds) for the memory required by pure and randomized observation-based strategies for each class of objectives.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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