True Concurrency Can Be Easy

TL;DR

The paper introduces step net bisimulation for finite Petri nets, simplifying the characterization of behavioral equivalences and establishing a logical framework for their analysis.

Contribution

It presents step net bisimulation as a simpler, coinductive relation that characterizes several existing bisimilarities without complex causality or bijections, and links it to a modal logic.

Findings

Step net bisimilarity is characterized by a modal logic called NML.

It provides a simpler alternative to existing behavioral equivalences.

The approach avoids complex causality structures and bijections.

Abstract

Step net bisimulation is a coinductive behavioral relation for finite Petri nets, which is a smooth generalization of the definition of standard step bisimulation \cite{NT84} on finite Petri nets. Its induced equivalence offers an alternative, much simpler characterization of causal-net bisimilarity \cite{G15,Gor22}, as it does not resort to any causality structure, and of structure-preserving bisimilarity \cite{G15}, as it does not require bijective mappings between related markings. We show that step net bisimilarity can be characterized logically by means of a suitable modal logic, called NML (acronym of net modal logic): two markings are step net bisimilar if and only if they satisfy the same NML formulae.