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Synthesis of Elementary Net Systems with Context Arcs and Localities

Koutny M., Pietkiewicz-Koutny M.

Fundamenta Informaticae

2008

Vol. 88, nr 3

307-328

We investigate the synthesis problem for ENCL-systems, defined as Elementary Net Systems extended with context (inhibitor and activator) arcs and explicit event localities. Since colocated events are meant to be executed synchronously, the behaviour of such systems is captured by step transition systems, where arcs are labelled by sets of events rather than by single events. We completely characterise transition systems generated by ENCL-systems after extending the standard notion of a region - defined as a certain set of states - with explicit information about events which, in particular, are responsible for crossing its border. As a result, we are able to construct, for each such transition system, a suitable ENCL-system generating it.

Synthesising Elementary Net Systems with Inhibitor Ares from Step Transition Systems

Pietkiewicz-Koutny M.

Fundamenta Informaticae

2002

Vol. 50, nr 2

175-203

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 (ENIapost). 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 ENIapost and ENI-systems (called respectively TSENIapost and TSENI transition systems).