Behavioural Equivalence for Infinite Systems - Partially Decidable!
نویسندگان
چکیده
For finite-state systems non-interleaving equivalences are computation-ally at least as hard as interleaving equivalences. In this paper we showthat when moving to infinite-state systems, this situation may changedramatically.We compare standard language equivalence for process description lan-guages with two generalizations based on traditional approaches captur-ing non-interleaving behaviour, pomsets representing global causal depen-dency, and locality representing spatial distribution of events.We first study equivalences on Basic Parallel Processes, BPP, a processcalculus equivalent to communication free Petri nets. For this simpleprocess language our two notions of non-interleaving equivalences agree.More interestingly, we show that they are decidable, contrasting a result ofHirshfeld that standard interleaving language equivalence is undecidable.Our result is inspired by a recent result of Esparza and Kiehn, showingthe same phenomenon in the setting of model checking.We follow up investigating to which extent the result extends to largersubsets of CCS and TCSP. We discover a significant difference betweenour non-interleaving equivalences. We show that for a certain non-trivialsubclass of processes between BPP and TCSP, not only are the two equiva-lences different, but one (locality) is decidable whereas the other (pomsets)is not. The decidability result for locality is proved by a reduction to thereachability problem for Petri nets.
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