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The Complexity of Partial-Observation Stochastic Parity Games with Finite-Memory Strategies

  • Krishnendu Chatterjee
  • Laurent Doyen
  • Sumit Nain
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)

Abstract

We consider two-player partial-observation stochastic games on finitestate graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are ε-regular conditions specified as parity objectives. The qualitative-analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). These qualitative-analysis problems are known to be undecidable. However in many applications the relevant question is the existence of finite-memory strategies, and the qualitative-analysis problems under finite-memory strategies was recently shown to be decidable in 2EXPTIME.We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis.

Keywords

Stochastic Game Winning Strategy Input Tree Tree Automaton Game Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Laurent Doyen
    • 2
  • Sumit Nain
    • 3
  • Moshe Y. Vardi
    • 3
  1. 1.IST AustriaAustria
  2. 2.CNRS, LSVENS CachanFrance
  3. 3.Rice UniversityUSA

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