Decidability Problems in Petri Nets with Names and Replication

In this paper we study decidability of several extensions of P/T nets with name creation and/or replication. In particular, we study how to restrict the models of RN systems (P/T nets extended with replication, for which reachability is undecidable) and ν-RN systems (RN extended with name creation, which are Turing-complete, so that coverability is undecidable), in order to obtain decidability of reachability and coverability, respectively. We prove that if we forbid synchronizations between the different components in a RN system, then reachability is still decidable. Similarly, if we forbid name communication between the different components in a ν-RN system, or restrict communication so that it is allowed only for a given finite set of names, we obtain decidability of coverability. Finally, we consider a polyadic version of ν-PN (P/T nets extended with name creation), that we call pν-PN, in which tokens are tuples of names. We prove that pν-PN are Turing complete, and discuss how the results obtained for ν-RN systems can be translated to them.

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