Coverability, Termination, and Finiteness in Recursive Petri Nets

Petri Nets Coverability

This assignment is concerned with the coverability problem in Petri nets. Formally, given a Petri net N with set of places P , a source marking ms in NP , and a target marking mt in NP , the problem asks whether there exists m in NP such that ms →N m and m ≥ mt. Here (and in the remainder of this assignment), the ordering is the product ordering over NP , defined by m ≤ m′ if and only if m(p) ≤...

Coverability Synthesis in Parametric Petri Nets

We study Parametric Petri Nets (PPNs), i.e., Petri nets for which some arc weights can be parameters. In that setting, we address a problem of parameter synthesis, which consists in computing the exact set of values for the parameters such that a given marking is coverable in the instantiated net. Since the emptiness of that solution set is already undecidable for general PPNs, we address a spe...

The Complexity of Coverability in nu-Petri Nets

We show that the coverability problem in ν-Petri nets is complete for ‘double Ackermann’ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes ν-Pe...

SAT-solving the Coverability Problem for Unbounded Petri Nets

Accelerations for the Coverability Set of Petri Nets with Names

Pure names are identifiers with no relation between them, except equality and inequality. In previous works we have extended P/T nets with the capability of creating and managing pure names, obtaining ν-PNs and proved that they are strictly well structured (WSTS), so that coverability and boundedness are decidable. Here we use the framework recently developed by Finkel and Goubault-Larrecq for ...