The Wadge Hierarchy of Petri Nets omega-Languages

Abstract : We describe the Wadge hierarchy of the omega-languages recognized by deterministic Petri nets. This is an extension of the celebrated Wagner hierarchy which turned out to be the Wadge hierarchy of the omega-regular languages. Petri nets are more powerful devices than finite automata. They may be defined as partially blind multi-counter automata. We show that the whole hierarchy has height $\omega^{\omega^2}$, and give a description of the restrictions of this hierarchy to partially blind multi-counter automata of some fixed positive number of counters.
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Jacques Duparc, Olivier Finkel, Jean-Pierre Ressayre. The Wadge Hierarchy of Petri Nets omega-Languages. Vasco Brattka, Hannes Diener, and Dieter Spreen. Logic, Computation, Hierarchies, Festschrift Volume in Honor of Victor Selivanov at the occasion of his sixtieth birthday., 4, De Gruyter, pp.109-138, 2014, Ontos Mathematical Logic, 978-1-61451-804-4. ⟨hal-00743510v3⟩

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