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Exploring probabilistic bisimulations, part I

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Formal Aspects of Computing

Abstract

We take a fresh look at strong probabilistic bisimulations for processes which exhibit both non-deterministic and probabilistic behaviour. We suggest that it is natural to interpret such processes as distributions over states in a probabilistic labelled transition system, a pLTS; this enables us to adapt the standard notion of contextual equivalence to this setting. We then prove that a novel form of bisimulation equivalence between distributions are both sound and complete with respect to this contextual equivalence. We also show that a very simple extension to HML, Hennessy–Milner Logic, provides finite explanations for inequivalences between distributions. Finally we show that our bisimulations between distributions in a pLTS are simply an alternative characterisation of a standard notion of probabilistic bisimulation equivalence, defined between states in a pLTS.

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Authors and Affiliations

  1. Department of Computer Science, Trinity College, Dublin 1, Ireland

    Matthew Hennessy

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  1. Matthew Hennessy
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Correspondence to Matthew Hennessy.

Additional information

Peter Höfner, Robert van Glabbeek and Ian Hayes

Supported financially by SFI project no. SFI 06 IN.1 1898.

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Hennessy, M. Exploring probabilistic bisimulations, part I. Form Asp Comp 24, 749–768 (2012). https://doi.org/10.1007/s00165-012-0242-7

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  • DOI: https://doi.org/10.1007/s00165-012-0242-7

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