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 rene it for quasi-discrete closure models. We also dene 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 renes 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.
On Bisimilarities for Closure Spaces - Preliminary Version
Ciancia V;Latella D;Massink M;
2021
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 rene it for quasi-discrete closure models. We also dene 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 renes 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.File | Dimensione | Formato | |
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Descrizione: CoRR, abs/2105.06690
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