University of Newcastle upon Tyne COMPUTING

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 the nets with range arcs. About the author Jetty Kleijn is a visiting fellow of the School of Computing Science, Newcastle University. Maciej Koutny obtained his MSc (1982) and PhD (1984) from the Warsaw University of Technology. In 1985 he joined the then Computing Laboratory of the University of Newcastle upon Tyne to work as a Research Associate. In 1986 he became a Lecturer in Computing Science at Newcastle, and in 1994 was promoted to an established Readership at Newcastle. In 2000 he became a Professor of Computing Science. Suggested keywords THEORY OF CONCURRENCY, PETRI NETS, WEIGHTED ACTIVATOR AND INHIBITOR ARCS, RANGE ARCS, CAUSALITY SEMANTICS, INFINITE PROCESSES, OCCURRENCE NETS, STEP SEQUENCES. Processes of Nets with Range Arcs Jetty Kleijn and Maciej Koutny 1 LIACS, Leiden University P.O.Box 9512, NL-2300 RA Leiden, The Netherlands [email protected] 2 School of Computing Science, University of Newcastle Newcastle upon Tyne, NE1 7RU, United Kingdom [email protected] 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 the nets with range arcs.