Persistent Permutability in Choice Petri Nets

TL;DR

This paper investigates the property of persistent permutability in choice Petri nets, establishing conditions under which it implies overall persistence and confirming Ochmanski's conjecture for certain classes.

Contribution

It identifies Petri net classes where persistent permutability guarantees persistence and proves Ochmanski's conjecture for these classes.

Findings

Persistent permutability implies persistence in certain Petri net classes.

The paper generalizes free-choice nets and relates to Petri's concept of confusion.

Ochmanski's conjecture is proven for these classes.

Abstract

Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and stating that a non-persistent sequence can be permuted into a persistent one. We identify Petri net classes for which persistent permutability already suffices to imply overall persistence. These classes generalise free-choice nets and are related to Petri's concept of ``confusion'', while they are distinguished from each other by diverse restrictions on the choice structure of a net. We prove Ochmanski's conjecture to be correct for these classes.