History Preserving Bisimulation for Contextual Nets

We investigate the notion of history preserving bisimulation for contextual P/T nets, a generalization of ordinary P/T Petri nets where a transition may check for the presence of tokens without consuming them (non-destructive read operations). A first equivalence, simply called HP-bisimulation, is based on Winskel’s prime event structures. A finer equivalence, called RHP-bisimulation (where “R” stands for “read”), relies on asymmetric event structures, a generalization of prime event structures which gives a more faithful account of the dependencies among transition occurrences arising in contextual net computations. Extending some previous work, we show that HP-bisimulation is decidable for finite n-safe contextual nets. Moreover by resorting to causal automata - a variation of ordinary automata introduced to deal with history dependent formalisms — we can obtain an algorithm for deciding HP-bisimulation and for getting a minimal realization. Decidability of RHP-bisimulation, instead, remains an open question.