In: Rapport de recherche, No. RR-3718, pages 1-32. Inria, June 1999. Available at http://www.inria.fr/RRRT/publications-fra.html.
Abstract: This paper investigates structural properties of occurrence (Petri) nets and their interpretation as unfolding semantics of Petri net systems. Occurrence nets (ONs) exhibit three kinds of node relations associated with causal ordering, concurrency, and conflict. We show that ONs can be decomposed in a natural way into substructures in each of which one or two of these relations are empty, namely: branches, trails, choices, lines, cuts certain density properties, i.e. non-empty intersections of substructures as above. On the semantic level, two established, yet non-equivalent, definitions of unfolding semantics are studied: branching processes (introduced by Engelfriet, Winskel et al.) and branching executions (Vogler). To both, the structural results apply, and both support appropriate partial order logics of high expressive power. We present two such logics that can be interpreted over occurrence net semantics of either kind: the branching time logic BLC and a non-branching logic LLC whose frame is composed of choices, i.e. objects representing horizons of mutually exclusive cuts (generalized global states) compatible with the corresponding phase.
Keywords: concurrency; Petri nets; semantics; branching processes.