Formal Verification of Petri Nets with Names

Abstract

Petri nets with name creation and management have been recently introduced so as to make Petri nets able to model the dynamics of (distributed) systems equipped with channels, cyphering keys, or computing boundaries. While traditional formal properties such as boundedness, coverability, and reachability, have been thoroughly studied for this class of Petri nets, formal verification against rich temporal properties has not been investigated so far. In this paper, we attack this verification problem. We introduce sophisticated variants of first-order \(\mu \)-calculus to specify rich properties that simultaneously account for the system dynamics and the names present in its states. We then analyse the (un)decidability boundaries for the verification of such logics, by considering different notions of boundedness. Notably, our decidability results are obtained via a translation to data-centric dynamic systems, a recently devised framework for the formal specification and verification of business processes working over relational database with constraints. In this light, our results contribute to the cross-fertilization between areas that have not been extensively related so far.