Synthesising Elementary Net Systems with Inhibitor Arcs from Step Transition Systems

Issue title: Application of Concurrency to System Design

Article type: Research Article

Authors: Pietkiewicz-Koutny, Marta

Affiliations: Department of Computing Science, University of Newcastle, Newcastle upon Tyne NE1 7RU, U.K.

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 synthesis problem for Elementary Net Systems with Inhibitor Arcs executed under the a-priori semantics (ENI) was solved in [18]. In this paper we completely characterise transition systems which can be generated by Elementary Net Systems with Inhibitor Arcs executed under the a-posteriori semantics (ENI_apost). 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 the 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. We then compare transition systems which are generated by ENI_apost and ENI-systems (called respectively TSENI_apost and TSENI transition systems).

Keywords: causality/partial order theory of concurrency, analysis and synthesis, structure and behaviour of nets, theory of regions, transition systems

Journal: Fundamenta Informaticae, vol. 50, no. 2, pp. 175-203, 2002