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.KeywordsEvent StructureFull SubcategoryLeft AdjointConservative ExtensionFiring SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.