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International Static Analysis Symposium

SAS 2005: Static Analysis pp 19–34Cite as

Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3672))

Abstract

A technique for generating invariant polynomial inequalities of bounded degree is presented using the abstract interpretation framework. It is based on overapproximating basic semi-algebraic sets, i.e., sets defined by conjunctions of polynomial inequalities, by means of convex polyhedra. While improving on the existing methods for generating invariant polynomial equalities, since polynomial inequalities are allowed in the guards of the transition system, the approach does not suffer from the prohibitive complexity of the methods based on quantifier-elimination. The application of our implementation to benchmark programs shows that the method produces non-trivial invariants in reasonable time. In some cases the generated invariants are essential to verify safety properties that cannot be proved with classical linear invariants.

This work has been partially supported by PRIN project “AIDA — Abstract Interpretation: Design and Applications,” by the “LogicTools” project (CICYT TIN 2004-03382), and the FPU grant AP2002-3693 from the Spanish MEC.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Parma, Italy

    Roberto Bagnara & Enea Zaffanella

  2. Software Department, Technical University of Catalonia, Spain

    Enric Rodríguez-Carbonell

Authors
  1. Roberto Bagnara
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  2. Enric Rodríguez-Carbonell
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  3. Enea Zaffanella
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Editor information

Editors and Affiliations

  1. Department of Computing, Imperial College London,  

    Chris Hankin

  2. Department of Computing, Imperial College London, 180 Queen’s Gate, SW7 2BZ, London, UK

    Igor Siveroni

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Bagnara, R., Rodríguez-Carbonell, E., Zaffanella, E. (2005). Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra. In: Hankin, C., Siveroni, I. (eds) Static Analysis. SAS 2005. Lecture Notes in Computer Science, vol 3672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11547662_4

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  • DOI: https://doi.org/10.1007/11547662_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28584-7

  • Online ISBN: 978-3-540-31971-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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