Section: New Results

Petri Nets and their Synthesis

Participant : Philippe Darondeau.

Petri Net Reachability Graphs: Decidability Status of FO Properties

In [24] , we investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order, modal and pattern-based languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques.

Separability in Persistent Petri Nets

We prove in [14] that the separability of plain, bounded, reversible and persistent Petri nets, a class of nets that extends the well-known live and bounded marked graphs. We establish first a weak form of separability, already known to hold for marked graphs, in which every firing sequence is simulated by a firing sequence of k parallel instances identical firing counts. We establish on top of this a strong form of separability, in which every firing sequence of is simulated by identical firing sequences.

Petri Net Distributability

A Petri net is distributed if, given an allocation of transitions to (geographical) locations, no two transitions at different locations share a common input place. A system is distributable if there is some distributed Petri net implementing it. We address in [23] the question of which systems can be distributed, while respecting a given allocation. The paper states the problem formally and discusses several examples illuminating — to the best of the authors' knowledge — the current status of this work.