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

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.

The above result appeared already in our technical report arXiv:2103.00729, although formulated and proven differently, since there we didn't have the preorder ${⊑}_1^{\infty }$, introduced in arXiv:2103.01490. Our revised proofs are conceptually simpler, as they avoid the auxiliary concepts of BD-runs and FS-runs

References in corpus (2)

• Abstract Processes of Place/Transition Systems
• Abstract Processes and Conflicts in Place/Transition Systems