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The Wadge Hierarchy of Petri Nets ω-Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7734))

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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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Author information

Authors and Affiliations

  1. Faculty of Business and Economics, University of Lausanne, CH-1015, Lausanne, Switzerland

    Jacques Duparc

  2. Equipe de Logique Mathématique, Institut de Mathématiques de Jussieu, CNRS et Université Paris 7, U.F.R. de Mathématiques, case 7012, site Chevaleret, 75205, Paris Cedex 13, France

    Olivier Finkel & Jean-Pierre Ressayre

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  1. Jacques Duparc
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  2. Olivier Finkel
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  3. Jean-Pierre Ressayre
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Editor information

Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, 10016, New York, NY, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, 14853, Ithaca, NY, USA

    Anil Nerode

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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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  • DOI: https://doi.org/10.1007/978-3-642-35722-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35721-3

  • Online ISBN: 978-3-642-35722-0

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