Regular paper
Studying equivalences of transition systems with algebraic tools

https://doi.org/10.1016/0304-3975(94)00047-MGet rights and content
Under an Elsevier user license
open archive

Abstract

The aim of this paper is twofold. On one side we will characterize observational equivalences (simulation, bisimulation) in an algebraic framework. On the other side we will deduce by this algebraic framework a new equivalence (the skeleton equivalence), which is an equivalence situated between trace equivalence and equality of languages.

In order to characterize simulation equivalence we will define a monad on the category of transition systems.

We introduce a category of algebras to characterize bisimulation. This category turns out to be the “Stone dual” of the category of transition systems. Moreover, this category of algebras seems to be a natural framework to reason about bisimulation equivalence; bisimulation corresponds to subalgebras isomorphisms and the minimal transition system in a bisimulation class corresponds to the minimal subalgebra of a given algebra.

Eventually the notion of minimal subalgebra will, roughly speaking, be factorized as the Boolean completion of the “skeleton” of an algebra, so that the concept of skeleton equivalence naturally arises.

Cited by (0)