Coincidence of two intermediate HDA bisimilarities

Determine whether the two higher-dimensional-automaton bisimulation equivalences for which the paper establishes inclusion but provides no separating example coincide.

Background

The paper introduces a family of bisimulation equivalences between ST-bisimilarity and hereditary history-preserving (hhp) bisimilarity by independently selecting requirements for subsumption, unsubsumption, similarity, and path restriction. It proves several strict inclusions among these equivalences using explicit higher-dimensional automata as separating examples.

For one pair of equivalences, however, only an inclusion is established and no counterexample separating the two notions is found. The authors therefore leave unresolved whether that inclusion is strict or whether the two equivalences actually coincide. The sentence stating the problem does not identify the pair by name.

References

Between two of the equivalences we establish inclusion without a separating example; hereby we pose the open question whether these equivalences coincide.

— Bisimulations and Modal Logics for Higher Dimensional Automata  (2608.14117 - Zouari et al., 14 Aug 2026) in Introduction, paragraph beginning “A spectrum of new bisimilarities”