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Characterizing Stable Inequalities of Petri Nets

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9115))

Abstract

One way to express correctness of a Petri net \(N\) is to specify a linear inequality \(U\), requiring each reachable marking of \(N\) to satisfy \(U\). A linear inequality \(U\) is stable if it is preserved along steps. If \(U\) is stable, then verifying correctness reduces to checking \(U\) in the initial marking of \(N\). In this paper, we characterize classes of stable linear inequalities of a given Petri net by means of structural properties. Thereby, we generalize classical results on traps, co-traps, and invariants. We show how to decide stability of a given inequality. For a certain class of inequalities, we present a polynomial time decision procedure.

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Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany

    Marvin Triebel & Jan Sürmeli

Authors
  1. Marvin Triebel
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  2. Jan Sürmeli
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Correspondence to Marvin Triebel .

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Editors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Raymond Devillers

  2. Tampere University of Technology, Tampere, Finland

    Antti Valmari

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Triebel, M., Sürmeli, J. (2015). Characterizing Stable Inequalities of Petri Nets. In: Devillers, R., Valmari, A. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2015. Lecture Notes in Computer Science(), vol 9115. Springer, Cham. https://doi.org/10.1007/978-3-319-19488-2_14

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  • DOI: https://doi.org/10.1007/978-3-319-19488-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19487-5

  • Online ISBN: 978-3-319-19488-2

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