On Bisimilarities for Closure Spaces - Preliminary Version

Abstract

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure models-we call the resulting equivalence CM-bisimilarity-and refine it for quasi-discrete closure models. We also define two additional notions of bisimilarity that are based on paths on space, namely Path-bisimilarity and Compatible Pathbisimilarity, CoPa-bisimilarity for short. The former expresses (unconditional) reachability, the latter refines it in a way that is reminishent of Stuttering Equivalence on transition systems. For each bisimilarity we provide a logical characterisation, using variants of SLCS. We also address the issue of (space) minimisation via the three equivalences.