Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach

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Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach (1998)

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by E.P. de Vink , J.J.M.M. Rutten

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102 - 15 self

BibTeX

@MISC{Vink98bisimulationfor,
    author = {E.P. de Vink and J.J.M.M. Rutten},
    title = {Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach},
    year = {1998}
}

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Abstract

. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...

Keyphrases

probabilistic transition system coalgebraic approach discrete probabilistic transition system probabilistic bisimilarity final coalgebra set functor basic process equivalence coalgebraic formulation probabilistic bisimulation abstract semantical domain skou ls91 reasonable condition van glabbeek reactive system borel probability measure borel measure final coalgebra paradigm coalgebraic definition continuous setting ultrametric space

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