Abstract
We describe the Wadge hierarchy of the ω-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 ω-regular languages. Petri nets are an improvement of 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 every fixed number of partially blind counters.
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Duparc, J., Finkel, O., Ressayre, JP. (2013). The Wadge Hierarchy of Petri Nets ω-Languages. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_13
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