Transition systems of Elementary Net Systems with inhibitor arcs

Abstract

We here consider transition systems of Elementary Net Systems with inhibitor arcs. There are basically two different types of non-interleaving semantics of such Petri nets, the a-posteriori and a-priori semantics. The former is an instance of the causal partial order semantics, and can be captured using means similar to those developed for ordinary safe nets. The latter is based on an extension of the partial order semantics which includes weak causality in addition to the standard causality relationship. In this paper we deal only with the a-priori semantics. Our aim is to completely characterise transition systems which can be generated by Elementary Net Systems with inhibitor arcs. This is achieved by adapting the notion of a step transition system, i.e. one in which arcs are labelled by sets of events executed concurrently. In developing our model, we follow the standard approach in which the relationship between nets and their transition systems is established via the notion of a region. We define, and show consistency of, two behaviour preserving translations between nets and transition systems. Our results can be used to provide the basis for an automatic synthesis of nets with inhibitor arcs from operational descriptions expressed in terms of transition systems.