Processes of Petri Nets with Range Testing

Issue title: Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz

Article type: Research Article

Authors: Kleijn, Jetty | Koutny, Maciej

Affiliations: LIACS, Leiden University, P.O. Box 9512, NL-2300 RA Leiden, The Netherlands. E-mail: kleijn@liacs.nl | School of Computing Science, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. E-mail: maciej.koutny@ncl.ac.uk

Abstract: We are concerned with causality semantics in the executions of Petri nets with range arcs. Range arcs combine (and subsume) the distinctive features of inhibitor and activator arcs, and each such arc provides a means of specifying a range (a finite or infinite interval of non-negative integers) for the number of tokens in a place which makes enabling of a given transition possible. We demonstrate that the existing treatment of causality developed for Petri nets with inhibitor arcs based on structures generalising partial orders can also be applied to nets with range arcs.

Keywords: theory of concurrency, Petri nets, weighted activator and inhibitor arcs, range arcs, causality semantics, infinite processes, occurrence nets, step sequences

Journal: Fundamenta Informaticae, vol. 80, no. 1-3, pp. 199-219, 2007