Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

TL;DR

This paper introduces methods for decomposing labelled transition systems into components using products and articulations, facilitating faster Petri net synthesis and enabling structured analysis of complex systems.

Contribution

It proposes two novel decomposition techniques, products and articulations, to improve Petri net synthesis efficiency and system analysis.

Findings

Decomposition techniques enable modular synthesis of Petri nets.

Structured transition systems improve synthesis performance analysis.

Methods facilitate divide-and-conquer Petri net synthesis.

Abstract

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.