Abstract Processes and Conflicts in Place/Transition Systems

TL;DR

This paper introduces a new class of Petri nets called structural conflict nets and defines abstract processes for them, simplifying the analysis of systems with multiple tokens by focusing on conflict-free cases.

Contribution

It identifies structural conflict nets where token multiplicity does not cause conflict-concurrency interplay and defines abstract processes as equivalence classes for these nets.

Findings

Largest abstract process exists iff the net is conflict-free.

Abstract processes simplify the analysis of token multiplicity.

Structural conflict nets exclude conflict-concurrency interplay.

Abstract

For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this concept for nets where places carry multiple tokens, by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. Here we identify a subclass of Petri nets, called structural conflict nets, where no interplay between conflict and concurrency due to token multiplicity occurs. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that there is a largest abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.