On the Decomposition of Regional Events in Elementary Systems

We study the relation between labelled transition systems and the corresponding partial orders of regions. In particular, we focus on the sets of their potential events, or labels on the transitions, providing them with a structure so as to reason about concurrency from the perspective of the observable properties of these systems. This is achieved by introducing the notion of minimal events, as the generators of such a structure of labels. We show that these events are sufficient to synthesize a transition system, such that its Regional Partial Order is isomorphic to the one obtained with the full set of events.