Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

TL;DR

This paper explores bisimulation in labeled state-to-function transition systems (FuTS) from a coalgebraic perspective, establishing a correspondence with behavioral equivalence and relating it to various quantitative process algebras.

Contribution

It provides a coalgebraic characterization of FuTS bisimulation and links it to behavioral equivalence across multiple quantitative process languages.

Findings

FuTS bisimilarity coincides with behavioral equivalence.

Established correspondence for major quantitative process algebras.

Unified coalgebraic framework for different FuTS classes.

Abstract

Labeled state-to-function transition systems, FuTS for short, are characterized by transitions which relate states to functions of states over general semirings, equipped with a rich set of higher-order operators. As such, FuTS constitute a convenient modeling instrument to deal with process languages and their quantitative extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is established stating that FuTS-bisimilarity coincides with behavioural equivalence of the associated functor. As generic examples, the equivalences underlying substantial fragments of major examples of quantitative process algebras are related to the bisimilarity of specific FuTS. The examples range from a stochastic process language, PEPA, to a language for Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a language for Markov Automata, MAL. The equivalences underlying these languages are related to the bisimilarity of their specific FuTS. By the correspondence result coalgebraic justification of the equivalences of these calculi is obtained. The specific selection of languages, besides covering a large variety of process interaction models and modelling choices involving quantities, allows us to show different classes of FuTS, namely so-called simple FuTS, combined FuTS, nested FuTS, and general FuTS.