Abstract Processes in the Absence of Conflicts in General Place/Transition Systems

TL;DR

This paper explores the relationship between different process representations in general place/transition systems, establishing a bijection and uniqueness results for nets without conflicts, advancing understanding of net behaviors.

Contribution

It introduces an order-respecting bijection between BD-processes and FS-processes in countable nets, and proves the existence of a unique largest BD-process in conflict-free nets.

Findings

Established a bijection between BD-processes and FS-processes.

Proved the existence of a unique largest BD-process in conflict-free nets.

Extended process theory to general nets without conflicts.

Abstract

Goltz and Reisig generalised Petri's concept of processes of one-safe Petri nets to general nets where places carry multiple tokens. BD-processes are equivalence classes of Goltz-Reisig processes connected through the swapping transformation of Best and Devillers; they can be considered as an alternative representation of runs of nets. Here we present an order respecting bijection between the BD-processes and the FS-processes of a countable net, the latter being defined -- in an analogous way -- as equivalence classes of firing sequences. Using this, we show that a countable net without binary conflicts has a (unique) largest BD-process.