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  • We consider a class of finite 1.5-player games (Markov decision processes) where the winning objectives are specified in the branching-time temporal logic qPECTL* (an extension of the qualitative PCTL*). We study decidability and complexity of existence of a winning strategy in these games. We identify a fragment of qPECTL* called detPECTL* for which the existence of a winning strategy is decidable in exponential time, and also the winning strategy can be computed in exponential time (if it exists). Consequently we show that every formula of qPECTL* can be translated to a formula of detPECTL* (in exponential time) so that the resulting formula is equivalent to the original one over finite Markov chains. From this we obtain that for the whole qPECTL*, the existence of a winning finite-memory strategy is decidable in double exponential time. An immediate consequence is that the existence of a winning finite-memory strategy is decidable for the qualitative fragment of PCTL* in triple exponential time.
  • We consider a class of finite 1.5-player games (Markov decision processes) where the winning objectives are specified in the branching-time temporal logic qPECTL* (an extension of the qualitative PCTL*). We study decidability and complexity of existence of a winning strategy in these games. We identify a fragment of qPECTL* called detPECTL* for which the existence of a winning strategy is decidable in exponential time, and also the winning strategy can be computed in exponential time (if it exists). Consequently we show that every formula of qPECTL* can be translated to a formula of detPECTL* (in exponential time) so that the resulting formula is equivalent to the original one over finite Markov chains. From this we obtain that for the whole qPECTL*, the existence of a winning finite-memory strategy is decidable in double exponential time. An immediate consequence is that the existence of a winning finite-memory strategy is decidable for the qualitative fragment of PCTL* in triple exponential time. (en)
Title
  • Strategy Synthesis for Markov Decision Processes and Branching-Time Logics
  • Strategy Synthesis for Markov Decision Processes and Branching-Time Logics (en)
skos:prefLabel
  • Strategy Synthesis for Markov Decision Processes and Branching-Time Logics
  • Strategy Synthesis for Markov Decision Processes and Branching-Time Logics (en)
skos:notation
  • RIV/00216224:14330/07:00022548!RIV10-MSM-14330___
http://linked.open...avai/riv/aktivita
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  • P(1M0545)
http://linked.open...vai/riv/dodaniDat
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  • 452659
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  • RIV/00216224:14330/07:00022548
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  • Markov decision processes; branching-time logics (en)
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  • [5D27CC9F5079]
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  • Lisabon
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  • Berlin Heidelberg New York
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  • Proceedings of 18th International Conference on Concurrency Theory (CONCUR 2007)
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  • Brázdil, Tomáš
  • Forejt, Vojtěch
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number of pages
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  • Springer-Verlag
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  • 978-3-540-74406-1
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  • 14330
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