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International Symposium on Automated Technology for Verification and Analysis

ATVA 2004: Automated Technology for Verification and Analysis pp 93–107Cite as

Disjunctive Invariants for Numerical Systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3299))

Abstract

We apply linear algebra techniques to over-approximate the reachability relation of a numerical system (Petri nets, counters automata, timed automata and so on) by a transitive and reflexive finite union of affine spaces. Thanks to this kind of approximation, we naturally define the notion of disjunctive place invariants. All the results presented in this paper have been implemented as a plug-in for our symbolic model-checker Fast and applied to the 40 systems available on the Fast-homepage.

Research funded by the Faculté des arts et des sciences of the Université de Montréal and by the Natural Sciences and Engineering Research Council of Canada through a discovery grant held by Pierre McKenzie.This work was partially carried out during the author’s doctoral studies at Lab. Specification and Verification, ENS-Cachan (FRANCE).

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Author information

Authors and Affiliations

  1. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, Pavillon André-Aisenstadt, CP 6128 succ Centre Ville, H3C 3J7, Montréal, QC, Canada

    Jérôme Leroux

Authors
  1. Jérôme Leroux
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Editor information

Editors and Affiliations

  1. Grad. Inst. of Electronic Engineering, National Taiwan University, Taiwan, ROC

    Farn Wang

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Leroux, J. (2004). Disjunctive Invariants for Numerical Systems. In: Wang, F. (eds) Automated Technology for Verification and Analysis. ATVA 2004. Lecture Notes in Computer Science, vol 3299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30476-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-30476-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23610-8

  • Online ISBN: 978-3-540-30476-0

  • eBook Packages: Springer Book Archive

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