Abstract processes of place/transition systems

• Published in: Information processing letters Vol. 111; no. 13; pp. 626 - 633
• Main Authors: van Glabbeek, Rob J., Goltz, Ursula, Schicke, Jens-Wolfhard
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2011; Elsevier; Elsevier Sequoia S.A
• Subjects: Algebra; Algorithmics. Computability. Computer arithmetics; Applied sciences; Causal semantics; Causality; Commutative rings and algebras; Computer science; control theory; systems; Concurrency; Exact sciences and technology; Language theory and syntactical analysis; Mathematical models; Mathematics; Miscellaneous; Optimization algorithms; P/T systems; Petri nets; Processes; Proposals; Recall; Sciences and techniques of general use; Studies; Theoretical computing; Causal semantics; Processes; Concurrency; Petri nets; P/T systems; Computer theory; History; Equivalence classes; Transition system; Semantics; Multiplicity; Information processing; Causality; Algorithm analysis; Petri net
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2011.03.013

A well-known problem in Petri net theory is to formalise an appropriate causality-based concept of process or run for place/transition systems. The so-called individual token interpretation, where tokens are distinguished according to their causal history, giving rise to the processes of Goltz and Reisig, is often considered too detailed. The problem of defining a fully satisfying more abstract concept of process for general place/transition systems has so-far not been solved. In this paper, we recall the proposal of defining an abstract notion of process, here called BD-process, in terms of equivalence classes of Goltz–Reisig processes, using an equivalence proposed by Best and Devillers. It yields a fully satisfying solution for at least all one-safe nets. However, for certain nets which intuitively have different conflicting behaviours, it yields only one maximal abstract process. Here we identify a class of place/transition systems, called structural conflict nets, where conflict and concurrency due to token multiplicity are clearly separated. We show that, in the case of structural conflict nets, the equivalence proposed by Best and Devillers yields a unique maximal abstract process only for conflict-free nets. Thereby BD-processes constitute a simple and fully satisfying solution in the class of structural conflict nets. ► We introduce the Petri net class of structural conflict nets (SCN). ► On SCNs, processes modulo Best/Devillers swapping give a satisfying semantics. ► This semantics adheres to the collective token interpretation and respects causality.