Decidability results for restricted models of petri nets with name creation and replication

Abstract

In previous works we defined ν-APNs, an extension of P/T nets with the capability of creating and managing pure names. We proved that, though reachability is undecidable, coverability remains decidable for them. We also extended P/T nets with the capability of nets to replicate themselves, creating a new component, initially marked in some fixed way, obtaining g-RN systems. We proved that these two extensions of P/T nets are equivalent, so that g-RN systems have undecidable reachability and decidable coverability. Finally, for the class of the so called ν-RN systems, P/T nets with both name creation and replication, we proved that they are Turing complete, so that also coverability turns out to be undecidable. In this paper we study how can we restrict the models of ν-APNs (and, therefore, g-RN systems) and ν-RN systems in order to keep decidability of reachability and coverability, respectively. We prove that if we forbid synchronizations between the different components in a g-RN system, then reachability is still decidable. The proof is done by reducing it to reachability in a class of multiset rewriting systems, similar to Recursive Petri Nets. Analogously, if we forbid name communication between the different components in a ν-RN system, or restrict communication to happen only for a given finite set of names, we obtain decidability of coverability.