Refinement and Asynchronous Composition of Modal Petri Nets

We propose a framework for the specification of infinite state systems based on Petri nets with distinguishedmayandmust-transitions (called modalities) which specify the allowed and the required behavior of refinements and hence of implementations. For any modal Petri net, we define its generated modal language specification which abstracts away silent transitions. On this basis we consider refinements of modal Petri nets by relating their generated modal language specifications. We show that this refinement relation is decidable if the underlying modal Petri nets are weakly deterministic. We also show that the membership problem for the class of weakly deterministic modal Petri nets is decidable. As an important application scenario of our approach we consider I/OPetri nets and their asynchronous composition which typically leads to an infinite state system.