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A Few Graph-Based Relational Numerical Abstract Domains

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Static Analysis (SAS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2477))

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Abstract

This article presents the systematic design of a class of relational numerical abstract domains from non-relational ones. Constructed domains represent sets of invariants of the form (v j - v i ∈ C), where vj and vi are two variables, and C lives in an abstraction of \( \mathcal{P}(\mathbb{Z}) \) , \( \mathcal{P}(\mathbb{Q}) \) , or \( \mathcal{P}(\mathbb{R}) \) . We will call this family of domains weakly relational domains. The underlying concept allowing this construction is an extension of potential graphs and shortest-path closure algorithms in exotic-like algebras. Example constructions are given in order to retrieve well-known domains as well as new ones. Such domains can then be used in the Abstract Interpretation framework in order to design various static analyses. A major benefit of this construction is its modularity, allowing to quickly implement new abstract domains from existing ones.

This work was supported in part by the RTD project IST-1999-20527 “DAEDALUS” of the European IST FP5 program.

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Author information

Authors and Affiliations

  1. École Normale Supérieure de Paris, France

    Antoine Miné

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  1. Antoine Miné
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Editors and Affiliations

  1. Department of Computer Science Facultad de Informática, Technical University of Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Madrid, Spain

    Manuel V. Hermenegildo  & Germán Puebla  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Miné, A. (2002). A Few Graph-Based Relational Numerical Abstract Domains. In: Hermenegildo, M.V., Puebla, G. (eds) Static Analysis. SAS 2002. Lecture Notes in Computer Science, vol 2477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45789-5_11

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  • DOI: https://doi.org/10.1007/3-540-45789-5_11

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  • Print ISBN: 978-3-540-44235-6

  • Online ISBN: 978-3-540-45789-3

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