Sequential and concurrent behaviour in Petri net theory
Theoretical Computer Science
Branching processes of Petri nets
Acta Informatica
Executions: a new partial-order semantics of Petri nets
Theoretical Computer Science
A trace semantics for Petri nets
Information and Computation
Concurrency, Modularity, and Synchronization
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
On the semantics of place/transition Petri nets
Mathematical Structures in Computer Science
The individual and collective token interpretations of Petri nets
CONCUR 2005 - Concurrency Theory
On causal semantics of Petri nets
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
On distributability of petri nets
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Hi-index | 0.89 |
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.