Structure Preserving Bisimilarity, Supporting an Operational Petri Net Semantics of CCSP

TL;DR

This paper introduces a new branching-time semantics called structure preserving bisimilarity for Petri net semantics of CCSP, which preserves causal structure and inevitability, and is a congruence for CCSP operators.

Contribution

It extends Olderog's Petri net semantics by employing structure preserving bisimilarity, a branching-time semantics that preserves causal structure and inevitability, and proves it as a congruence.

Findings

Structure preserving bisimilarity is a congruence for CCSP operators.

It preserves causal structure and inevitability in Petri net semantics.

The semantics strengthens previous linear-time equivalences.

Abstract

In 1987 Ernst-R\"udiger Olderog provided an operational Petri net semantics for a subset of CCSP, the union of Milner's CCS and Hoare's CSP. It assigns to each process term in the subset a labelled, safe place/transition net. To demonstrate the correctness of the approach, Olderog established agreement (1) with the standard interleaving semantics of CCSP up to strong bisimulation equivalence, and (2) with standard denotational interpretations of CCSP operators in terms of Petri nets up to a suitable semantic equivalence that fully respects the causal structure of nets. For the latter he employed a linear-time semantic equivalence, namely having the same causal nets. This paper strengthens (2), employing a novel branching-time version of this semantics---structure preserving bisimilarity---that moreover preserves inevitability. I establish that it is a congruence for the operators of CCSP.