D-Continuity and Petri’s Axioms of Concurrency for Nonsequential Process Models

Abstract

A non-sequential process can be modelled by a partially ordered set. Conversely, one is led to study the properties to be fulfilled by a poset so that it can reasonably be viewed as the model of a non-sequential process. To this end, C.A. Petri has proposed a set of con currency axioms and a related property called D-continuity, a generalised version for partially ordered sets of Dedekind’s completeness property of the real numbers. In this paper we study Petri’s axioms of concurrency and some of their interdependencies. We also derive several characterisations of D-continuity and exhibit its relation with the axioms of concurrency. Furthermore we apply our work to Petri nets: we introduce occurrence nets, some special posets which model the processes of a system net and we present their relations to D-continuity and the axioms of con currency. Finally we identify the class of the system nets whose processes are D-continuous and satisfy the axioms of concurrency.