History-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps

Abstract : One of the popular notions of equivalence for non-interleaving concurrent systems is history-preserving bisimilarity (hp-bisimilarity). Higher-dimensional automata (HDA) is a non-interleaving formalism for reasoning about behavior of concurrent systems, which provides a generalization (up to hp-bisimilarity) to the main models of concurrency proposed in the literature. Using open maps, we can show that hp-bisimilarity for HDA has a characterization directly in terms of (higher-dimensional) transitions of the HDA, rather than in terms of runs as e.g. for Petri nets. Our results imply decidability of hp-bisimilarity for finite HDA. They also put hp-bisimilarity firmly into the open-maps framework and tighten the connections between bisimilarity and weak topological fibrations.