An Operational Petri Net Semantics for the Join-Calculus

Stephan Mennicke
(TU Braunschweig)

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this gap by providing an abstract specification language which is asynchronously distributable. Classical process semantics establish an implicit order of actually independent actions, by means of an interleaving. So does the semantics of the join-calculus. To capture such independent actions, step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri net semantics for the join-calculus induces step-behavior in a natural way. We prove our semantics behaviorally equivalent to the original join-calculus semantics by means of a bisimulation. We discuss how join specific assumptions influence an existing notion of distributability based on Petri nets.

In Bas Luttik and Michel A. Reniers: Proceedings Combined 19th International Workshop on Expressiveness in Concurrency and 9th Workshop on Structured Operational Semantics (EXPRESS/SOS 2012), Newcastle upon Tyne, UK, September 3, 2012, Electronic Proceedings in Theoretical Computer Science 89, pp. 131–147.
Published: 12th August 2012.

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