A Spectrum of Behavioral Relations over LTSs on Probability Distributions

  • Silvia Crafa
  • Francesco Ranzato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6901)


Probabilistic nondeterministic processes are commonly modeled as probabilistic LTSs (PLTSs, a.k.a. probabilistic automata). A number of logical characterizations of the main behavioral relations on PLTSs have been studied. In particular, Parma and Segala [2007] define a probabilistic Hennessy-Milner logic interpreted over distributions, whose logical equivalence/preorder when restricted to Dirac distributions coincide with standard bisimulation/simulation between the states of a PLTS. This result is here extended by studying the full logical equivalence/preorder between distributions in terms of a notion of bisimulation/simulation defined on a LTS of probability distributions (DLTS). We show that the standard spectrum of behavioral relations on nonprobabilistic LTSs as well as its logical characterization in terms of Hennessy-Milner logic scales to the probabilistic setting when considering DLTSs.


Modal Logic Abstract Interpretation Diamond Operator Abstract Domain Symmetric Relation 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Silvia Crafa
    • 1
  • Francesco Ranzato
    • 1
  1. 1.University of PadovaItaly

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