2021/05/14 by Vincenzo Ciancia, Ciancia, Vincenzo, Diego Latella +2
Computer Science · Mathematics · #68Q60 #Advanced Banach Space Theory #Computational Geometry and Mesh Generation #D.2.4 #Digital Image Processing Techniques #F.4.1 #FOS: Computer and information sciences #I.2.4 #I.4.6 #Logic in Computer Science (cs.LO)
paper · pdf · doi:10.48550/arxiv.2105.06690
openalex publication_date 2021/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Path-bisimilarity, 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 the Spatial Logic for Closure Spaces (SLCS). We also address the issue of (space) minimisation via the three equivalences.