Synchronization in petri nets

Abstract

In "Petri nets are Monoids" by Meseguer and Montanari, categories for Petri nets with and without markings are introduced, where the categorical product and coproduct express the joint behavior of nets. However, this framework lacks structure in the sense that there is no categorical technique to define a composition of nets satisfying some given synchronization specification. In this paper, a synchronization operation is proposed which is a functor induced by some given synchronization prescription at the transition levei. Moreover, since this operation is also able to represent the asynchronous composition, the fact that some categories of Petri nets lack coproducts (asynchronous composition) is not anymore a restriction for interaction semantics.