Asynchronous Traces and Open Petri Nets
The relation between process calculi and Petri nets, two fundamental models of concurrency, has been widely investigated. Many proposals exist for encoding process calculi into Petri nets while preserving some behavioural features of interest. We recently introduced a framework where a net encoding can be defined uniformly for calculi with different communication patterns, including synchronous two-party, multi-party, and asynchronous communication. The encoding preserves and reflects several behavioural semantics, notably bisimulation equivalence. The situation is less immediate for asynchronous calculi and trace semantics: considering traces that arise when viewing asynchronous calculi as a fragment of the synchronous ones, trace equivalence is not reflected by the encoding. Focusing on CCS, we argue that this phenomenon is related to the imperfect match between trace inclusion and may testing preorder. We consider an alternative labelled transition systems where the latter issue is solved, and we show that, indeed, the corresponding trace semantics is preserved and reflected by the net encoding.
KeywordsAsynchronous CCS (Open) Petri nets Modular encoding May testing Trace semantics
We are indebted in many ways to Pierpaolo Degano. Indeed, the earliest exposure of the third author to Petri nets was in a remote cycle of seminars, whose initial lesson was introduced by the quotation in the first page. A scary moment, if there ever was one. Along the years, we all –either as Ph.D. students or later on as co-authors/colleagues/partners in projects– benefited from the insights and availability of Pierpaolo. More technically, we already mentioned his early contributions on net encoding for calculi. In general terms, the insistence on the proof structure of a computation in order to distill a suitable (concurrent) semantics for a calculus, which is typical of the work of Pierpaolo since the early Eighties, has been a fixed star: the modularity of our net encoding spills out of this “commandment”.
We are most grateful to the anonymous reviewers whose suggestions and remarks helped us to improve the paper.
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