Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

TL;DR

This paper introduces a framework for reconfiguring Petri nets while preserving their behavior, using open nets and bisimilarity notions that account for interactions with the environment.

Contribution

It develops a colimit-based composition for open Petri nets and proves bisimilarity as a congruence, enabling behavior-preserving reconfigurations.

Findings

Bisimilarity over open nets is a congruence with respect to composition.

The framework supports different observational equivalences, including weak bisimilarity.

Reconfiguration rules can be identified that preserve observational semantics.

Abstract

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.