International Journal of Foundations of Computer Science 3, 4, (1992) 443-478.
Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step.
Petri nets (or Place/Transition nets) give rise to such step transition systems in a natural way-the marking diagram of a Petri net is the canonical transition system associated with it. In this paper, we characterize the class of PN-transition systems, which are precisely those step transition systems generated by Petri nets.
We express the correspondence between PN-transition systems and Petri nets in terms of an adjunction between a category of PN-transition systems and a category of Petri nets in which the associated morphisms are behaviour-preserving in a strong and natural sense.