Attractor Basins in Concurrent Systems

TL;DR

This paper presents an algorithm for identifying attraction basins in safe Petri nets, helping analyze long-term behaviors and irreversible choices in concurrent systems using net unfoldings.

Contribution

It introduces a novel method to determine attraction basins in safe Petri nets, extending previous work on attractors with a new algorithm based on net unfoldings.

Findings

Successfully maps configurations leading to fatal basins.

Provides a systematic way to analyze irreversible behaviors.

Enhances understanding of long-run dynamics in concurrent systems.

Abstract

A crucial question in analyzing a concurrent system is to determine its long-run behaviour, and in particular, whether there are irreversible choices in its evolution, leading into parts of the reachability space from which there is no return to other parts. Casting this problem in the unifying framework of safe Petri nets, our previous work has provided techniques for identifying attractors, i.e. terminal strongly connected components of the reachability space. What we aim at is to determine the attraction basins associated to those attractors; that is, those states from where all infinite runs are doomed to end in the given attractor, as opposed to those that are free to evolve differently. Here, we provide a solution for the case of safe Petri nets. Our algorithm uses net unfoldings and provides a map of all of those configurations (concurrent executions of the system) that lead onto cliff-edges, i.e. any maximal extension for those configurations lies in some basin that is considered fatal.