A Definition Scheme for Quantitative Bisimulation

Diego Latella
(CNR/ISTI, Pisa)
Mieke Massink
(CNR/ISTI, Pisa)
Erik de Vink
(TU/e, Eindhoven)

FuTS, state-to-function transition systems are generalizations of labeled transition systems and of familiar notions of quantitative semantical models as continuous-time Markov chains, interactive Markov chains, and Markov automata. A general scheme for the definition of a notion of strong bisimulation associated with a FuTS is proposed. It is shown that this notion of bisimulation for a FuTS coincides with the coalgebraic notion of behavioral equivalence associated to the functor on Set given by the type of the FuTS. For a series of concrete quantitative semantical models the notion of bisimulation as reported in the literature is proven to coincide with the notion of quantitative bisimulation obtained from the scheme. The comparison includes models with orthogonal behaviour, like interactive Markov chains, and with multiple levels of behavior, like Markov automata. As a consequence of the general result relating FuTS bisimulation and behavioral equivalence we obtain, in a systematic way, a coalgebraic underpinning of all quantitative bisimulations discussed.

In Nathalie Bertrand and Mirco Tribastone: Proceedings Thirteenth Workshop on Quantitative Aspects of Programming Languages and Systems (QAPL 2015), London, UK, 11th-12th April 2015, Electronic Proceedings in Theoretical Computer Science 194, pp. 63–78.
Published: 28th September 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.194.5 bibtex PDF
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