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arXiv · 2608.14117

Bisimulations and Modal Logics for Higher Dimensional Automata

Safa Zouari·Rob van Glabbeek·Krzysztof Ziemiański
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Abstract

Higher-Dimensional Automata (HDAs) provide a geometric model of true concurrency. While hereditary history-preserving (hhp) bisimilarity is the finest behavioural equivalence in van Glabbeek's spectrum, no modal logic has previously characterised it on HDAs. We introduce several new intermediate equivalences that sit strictly between ST- and hhp-bisimilarity. We show how separating similarity and subsumption of paths leads to a clean formulation of these equivalences, and we present a modal logic that characterises hhp-bisimilarity. Natural fragments characterise ST-bisimilarity and the intermediate notions.

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Safa Zouari, Rob van Glabbeek, Krzysztof Ziemiański. 2026-08-14. Bisimulations and Modal Logics for Higher Dimensional Automata. https://doi.org/10.4230/lipics.concur.2026.49

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