A hierarchy of probabilistic system types

  • Authors:

  • Falk Bartels;Ana Sokolova;Erik de Vink

  • Affiliations:

  • CWI, Amsterdam, The Netherlands;Eindhoven University of Technology, The Netherlands;Eindhoven University of Technology, The Netherlands and Leiden University, The Netherlands

  • Venue:
  • Theoretical Computer Science - Selected papers of CMCS'03
  • Year:
  • 2004

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Abstract

We arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy. Our expressiveness criterion is the existence of a system translation, from the less expressive type into the more expressive type, that preserves and reflects probabilistic bisimilarity. We model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature. The theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy. All these translations arise in a standard way from natural transformations between the two behaviour functors involved. Such a translation generally preserves coalgebraic bisimilarity. We exploit a new result that, under mild assumptions on the behaviour functors, a system translation induced by a natural transformation with injective components also reflects bisimilarity.