A Definition Scheme for Quantitative Bisimulation

TL;DR

This paper introduces a unified scheme for defining strong bisimulation in FuTS, showing its equivalence with coalgebraic behavioral equivalence and unifying various quantitative models.

Contribution

It proposes a general definition scheme for quantitative bisimulation in FuTS, linking it with coalgebraic concepts and unifying existing models.

Findings

The bisimulation notion for FuTS coincides with coalgebraic behavioral equivalence.

The scheme applies to models like Markov chains, Markov automata, and interactive Markov chains.

The approach provides a systematic coalgebraic foundation for all discussed quantitative bisimulations.

Abstract

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.