Don’t Know in Probabilistic Systems

  • Harald Fecher
  • Martin Leucker
  • Verena Wolf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3925)


In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstract Markov chains) with respect to specifications in probabilistic temporal logics, interpreted over a 3-valued domain. More specifically, we introduce a 3-valued version of probabilistic computation-tree logic (PCTL) and give a model checking algorithm w.r.t. abstract Markov chains.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Harald Fecher
    • 1
  • Martin Leucker
    • 2
  • Verena Wolf
    • 3
  1. 1.Institute of InformaticsUniversity of KielGermany
  2. 2.Institute of InformaticsTU MunichGermany
  3. 3.Institute of InformaticsUniversity of MannheimGermany

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