A General Framework for Probabilistic Characterizing Formulae

  • Joshua Sack
  • Lijun Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7148)


Recently, a general framework on characteristic formulae was proposed by Aceto et al. It offers a simple theory that allows one to easily obtain characteristic formulae of many non-probabilistic behavioral relations. Our paper studies their techniques in a probabilistic setting. We provide a general method for determining characteristic formulae of behavioral relations for probabilistic automata using fixed-point probability logics. We consider such behavioral relations as simulations and bisimulations, probabilistic bisimulations, probabilistic weak simulations, and probabilistic forward simulations. This paper shows how their constructions and proofs can follow from a single common technique.


Weight Function Model Check Complete Lattice Label Transition System Forward Simulation 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joshua Sack
    • 1
  • Lijun Zhang
    • 2
  1. 1.Department of Mathematics and StatisticsCalifornia State University Long BeachUSA
  2. 2.DTU InformaticsTechnical University of DenmarkDenmark

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