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International Workshop on Verification, Model Checking, and Abstract Interpretation

VMCAI 2012: Verification, Model Checking, and Abstract Interpretation pp 235–250Cite as

Donut Domains: Efficient Non-convex Domains for Abstract Interpretation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7148))

Abstract

Program analysis using abstract interpretation has been successfully applied in practice to find runtime bugs or prove software correct. Most abstract domains that are used widely rely on convexity for their scalability. However, the ability to express non-convex properties is sometimes required in order to achieve a precise analysis of some numerical properties. This work combines already known abstract domains in a novel way in order to design new abstract domains that tackle some non-convex invariants. The abstract objects of interest are encoded as a pair of two convex abstract objects: the first abstract object defines an over-approximation of the possible reached values, as is done customarily. The second abstract object under-approximates the set of impossible values within the state-space of the first abstract object. Therefore, the geometrical concretization of our objects is defined by a convex set minus another convex set (or hole). We thus call these domains donut domains.

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Author information

Authors and Affiliations

  1. NEC Laboratories America, Inc., USA

    Khalil Ghorbal, Franjo Ivančić, Gogul Balakrishnan & Aarti Gupta

  2. NEC Corporation, Kanagawa, 211-8666, Japan

    Naoto Maeda

Authors
  1. Khalil Ghorbal
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  2. Franjo Ivančić
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  3. Gogul Balakrishnan
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  4. Naoto Maeda
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  5. Aarti Gupta
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Editor information

Editors and Affiliations

  1. Swiss Federal Institute of Technology Lausanne (EPFL), IC IIF LARA INR 318, Station 14, 1015, Lausanne, Switzerland

    Viktor Kuncak

  2. Institut für Informatik, Technische Universität München, Boltzmannstr. 3, 85748, Munich, Germany

    Andrey Rybalchenko

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Ghorbal, K., Ivančić, F., Balakrishnan, G., Maeda, N., Gupta, A. (2012). Donut Domains: Efficient Non-convex Domains for Abstract Interpretation. In: Kuncak, V., Rybalchenko, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2012. Lecture Notes in Computer Science, vol 7148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27940-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-27940-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27939-3

  • Online ISBN: 978-3-642-27940-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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