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Hasse Diagram Generators and Petri Nets

Oliveira Oliveira M.de

Fundamenta Informaticae

2011

Vol. 105, nr 3

263-289

In [18] Lorenz and Juh'as raised the question of whether there exists a suitable formalism for the representation of infinite families of partial orders generated by Petri nets. Restricting ourselves to bounded p/t-nets, we propose Hasse diagram generators as an answer. We show that Hasse diagram generators are expressive enough to represent the partial order language of any bounded p/t net. We prove as well that it is decidable both whether the (possibly infinite) family of partial orders represented by a given Hasse diagram generator is included in the partial order language of a given p/t-net and whether their intersection is empty. Based on this decidability result, we prove that the partial order languages of two given Petri nets can be effectively compared with respect to inclusion. Finally we address the synthesis of k-safe p/t-nets from Hasse diagram generators.

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).