An Operational Petri Net Semantics for the Join-Calculus

TL;DR

This paper introduces a Petri net-based operational semantics for the join-calculus, effectively modeling concurrent behaviors and bridging the gap between system specifications and implementations.

Contribution

It provides a novel Petri net semantics for the join-calculus that captures independent actions and demonstrates behavioral equivalence with the original semantics.

Findings

Petri net semantics naturally induce step-behavior.

Semantic equivalence established via bisimulation.

Discussion on join-specific assumptions affecting distributability.

Abstract

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.