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PVS Linear Algebra Libraries for Verification of Control Software Algorithms in C/ACSL

  • Heber Herencia-Zapana
  • Romain Jobredeaux
  • Sam Owre
  • Pierre-Loïc Garoche
  • Eric Feron
  • Gilberto Perez
  • Pablo Ascariz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7226)

Abstract

The problem of ensuring control software properties hold on their actual implementation is rarely tackled. While stability proofs are widely used on models, they are never carried to the code. Using program verification techniques requires express these properties at the level of the code but also to have theorem provers that can manipulate the proof elements. We propose to address this challenge by following two phases: first we introduce a way to express stability proofs as C code annotations; second, we propose a PVS linear algebra library that is able to manipulate quadratic invariants, i.e., ellipsoids. Our framework achieves the translation of stability properties expressed on the code to the representation of an associated proof obligation (PO) in PVS. Our library allows us to discharge these POs within PVS.

Keywords

Linear Algebra Proof Obligation Proof Assistant Theory Interpretation Excessive Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Heber Herencia-Zapana
    • 1
  • Romain Jobredeaux
    • 2
  • Sam Owre
    • 3
  • Pierre-Loïc Garoche
    • 4
  • Eric Feron
    • 2
  • Gilberto Perez
    • 5
  • Pablo Ascariz
    • 5
  1. 1.National Institute of AerospaceHamptonUnited States
  2. 2.Georgia Institute of TechnologyAtlantaUnited States
  3. 3.SRI InternationalMenlo ParkUnited States
  4. 4.The French Aerospace LabONERAToulouseFrance
  5. 5.University of A CoruñaCoruñaSpain

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