Local event structures and Petri nets

Abstract

In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? We provide a partial answer to this question here. Our answer is partial in that we propose a new class of event structures, called OL-event structures, and show that OLevent structures can be used to represent the behaviour of Petri nets, provided auto-concurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a nontrivial and conservative extension of the (prime) event structure semantics of 1-safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1-safe Petri nets established in a categorical framework in [W2] can be extended to the present setting, provided we restrict our attention to the subclass of Petri nets whose behaviours do not exhibit any auto-concurrency.