Petri Net Reachability Graphs: Decidability Status of First Order Properties

TL;DR

This paper analyzes the decidability and complexity of model-checking first-order properties on Petri net reachability graphs, providing systematic borders between decidable and undecidable cases.

Contribution

It offers a systematic analysis of decidability boundaries for first-order properties on Petri net reachability graphs using robust proof techniques.

Findings

Decidable cases are precisely characterized based on parameters.

Undecidability results are established for certain classes of properties.

The proof techniques demonstrate robustness across various parameters.

Abstract

We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on markings. We consider several parameters to separate decidable problems from undecidable ones. Not only are we able to provide precise borders and a systematic analysis, but we also demonstrate the robustness of our proof techniques.