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The Theory of WSTS: The Case of Complete WSTS

  • Conference paper
Application and Theory of Petri Nets (PETRI NETS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7347))

Abstract

We describe a simple, conceptual forward analysis procedure for ∞-complete WSTS \(\mathfrak S\). This computes the so-called clover of a state. When \(\mathfrak S\) is the completion of a WSTS \(\mathfrak X\), the clover in \(\mathfrak S\) is a finite description of the downward closure of the reachability set. We show that such completions are ∞-complete exactly when \(\mathfrak X\) is an ω 2 -WSTS, a new robust class of WSTS. We show that our procedure terminates in more cases than the generalized Karp-Miller procedure on extensions of Petri nets. We characterize the WSTS where our procedure terminates as those that are clover-flattable. Finally, we apply this to well-structured Presburger counter systems.

This paper is an extended abstract of a complete paper that will appear in the journal LMCS [FG12b]. A short version has already appeared in [FG09b] at ICALP’09.

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  1. ENS Cachan, France

    Alain Finkel & Jean Goubault-Larrecq

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  1. Alain Finkel
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  2. Jean Goubault-Larrecq
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  1. Laboratoire Spécification et Vérification, Ecole Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235, Cachan, France

    Serge Haddad

  2. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano–Bicocca, Viale Sarca, 336, 20126, Milano, Italy

    Lucia Pomello

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Finkel, A., Goubault-Larrecq, J. (2012). The Theory of WSTS: The Case of Complete WSTS. In: Haddad, S., Pomello, L. (eds) Application and Theory of Petri Nets. PETRI NETS 2012. Lecture Notes in Computer Science, vol 7347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31131-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-31131-4_2

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