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Generating Invariants for Non-linear Hybrid Systems by Linear Algebraic Methods

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Static Analysis (SAS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6337))

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Abstract

We describe powerful computational methods, relying on linear algebraic methods, for generating ideals for non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces by encoding the new consecution requirements as specific morphisms represented by matrices. More specifically, we establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our methods also embody a strategy to estimate degree bounds, leading to the discovery of rich classes of inductive, i.e. provable, invariants. Our approach avoids first-order quantifier elimination, Grobner basis computation or direct system resolution, thereby circumventing difficulties met by other recent techniques.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, University of Lugano, Switzerland

    Rachid Rebiha

  2. Institue de Mathematiques de Jussieu, Université Paris 7, Denis Diderot, France

    Nadir Matringe

  3. Institute of Computing, University of Campinas, SP, Brasil

    Arnaldo Vieira Moura & Rachid Rebiha

Authors
  1. Nadir Matringe
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  2. Arnaldo Vieira Moura
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  3. Rachid Rebiha
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Editor information

Editors and Affiliations

  1. Départment d’Informatique, École normale supérieure, rue d’Ulm 45, 75230, Paris cedex, France

    Radhia Cousot

  2. ELIAUS-DALI Laboratory, Université de Perpignan Via Domitia, 52, avenue Paul Alduy, 66860, Perpignan cedex, France

    Matthieu Martel

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Matringe, N., Moura, A.V., Rebiha, R. (2010). Generating Invariants for Non-linear Hybrid Systems by Linear Algebraic Methods. In: Cousot, R., Martel, M. (eds) Static Analysis. SAS 2010. Lecture Notes in Computer Science, vol 6337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15769-1_23

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  • DOI: https://doi.org/10.1007/978-3-642-15769-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15768-4

  • Online ISBN: 978-3-642-15769-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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