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SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities

  • Conference paper
Verification, Model Checking, and Abstract Interpretation (VMCAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5403))

Abstract

We introduce Subpolyhedra (SubPoly) a new numerical abstract domain to infer and propagate linear inequalities. Subpoly is as expressive as Polyhedra, but it drops some of the deductive power to achieve scalability. Subpoly is based on the insight that the reduced product of linear equalities and intervals produces powerful yet scalable analyses. Precision can be recovered using hints. Hints can be automatically generated or provided by the user in the form of annotations.

We implemented Subpoly on the top of Clousot, a generic abstract interpreter for .Net. Clousot with Subpoly analyzes very large and complex code bases in few minutes. Subpoly can efficiently capture linear inequalities among hundreds of variables, a result well-beyond state-of-the-art implementations of Polyhedra.

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Author information

Authors and Affiliations

  1. École Normale Supérieure, 45, rue d’Ulm, Paris, France

    Vincent Laviron

  2. Microsoft Research, Redmond, WA, USA

    Francesco Logozzo

Authors
  1. Vincent Laviron
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  2. Francesco Logozzo
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Editor information

Editors and Affiliations

  1. (Emeritus University of Copenhagen), Bukkeballevej 88, 2960, Rungsted, Denmark

    Neil D. Jones

  2. Institut für Informatik, Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität, 48149, Münster, Germany

    Markus Müller-Olm

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Laviron, V., Logozzo, F. (2008). SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities. In: Jones, N.D., Müller-Olm, M. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2009. Lecture Notes in Computer Science, vol 5403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93900-9_20

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  • DOI: https://doi.org/10.1007/978-3-540-93900-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-93899-6

  • Online ISBN: 978-3-540-93900-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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