Abstract Processes and Conflicts in Place/Transition Systems
Abstract
For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this concept for nets where places carry multiple tokens, by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. Here we identify a subclass of Petri nets, called structural conflict nets, where no interplay between conflict and concurrency due to token multiplicity occurs. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that there is a largest abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
Keywords
Cite
@article{arxiv.2103.01490,
title = {Abstract Processes and Conflicts in Place/Transition Systems},
author = {Rob van Glabbeek and Ursula Goltz and Jens-Wolfhard Schicke-Uffmann},
journal= {arXiv preprint arXiv:2103.01490},
year = {2021}
}
Comments
The results of this paper appeared before in arXiv:2103.00729. However, there they were formulated differently, as we didn't have the current concept of a largest abstract process. Our proofs are conceptually much simpler than the ones in arXiv:2103.00729, as they are carried out directly on abstract processes, rather than via the auxiliary concepts of BD-runs and FS-runs. arXiv admin note: text overlap with arXiv:1103.5916