Abstract
History preserving bisimilarity and maximality preserving bisimilarity take full account of the interplay between causality and branching, and they are congruences w.r.t. action refinement for suitable classes of Petri nets. But even for finite safe Petri nets they are based on possibly infinite transition systems, and it is not obvious how to decide them. OM-bisimulation gives a characterization of history preserving bisimulation for safe nets without internal moves, and it allows a decidability result. In this paper we generalize OM-bisimulation and this decidability result to safe nets with internal moves, and also treat the case of maximality preserving bisimulation.
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