Generalized Vietoris Bisimulations

TL;DR

This paper introduces a new form of bisimulation for coalgebras on Stone spaces, proving it is both sound and complete for behavioral equivalence and generalizes previous Vietoris bisimulations.

Contribution

It generalizes Vietoris bisimulations to Stone space coalgebras and shows that such bisimulations are topological closures of set-based bisimulations.

Findings

Bisimulation for Stone coalgebras is sound and complete.

The new bisimulation generalizes Vietoris bisimulations.

Bisimulation on Stone spaces is the topological closure of set-based bisimulation.

Abstract

We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that bisimulation for a $\mathbf{Stone}$ coalgebra is the topological closure of bisimulation for the underlying $\mathbf{Set}$ coalgebra.