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A New Numerical Abstract Domain Based on Difference-Bound Matrices

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Programs as Data Objects (PADO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2053))

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Abstract

This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x − y = c) and (±x = c) , where x and y are variables values and c is an integer or real constant.

Abstract elements are represented by Difference-Bound Matrices, widely used by model-checkers, but we had to design new operators to meet the needs of abstract interpretation. The result is a complete lattice of infinite height featuring widening, narrowing and common transfer functions. We focus on giving an efficient O(n 2)re presentation and graph-based O(n 3)algorit hms—where n is the number of variables—and claim that this domain always performs more precisely than the well-known interval domain.

To illustrate the precision/cost tradeoff of this domain, we have implemented simple abstract interpreters for toy imperative and parallel languages which allowed us to prove some non-trivial algorithms correct.

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Author information

Authors and Affiliations

  1. École Normale Supérieure de Paris, France

    Antoine Miné

Authors
  1. Antoine Miné
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Editor information

Editors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Building 540, 8000, Aarhus, Denmark

    Olivier Danvy  & Andrzej Filinski  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Miné, A. (2001). A New Numerical Abstract Domain Based on Difference-Bound Matrices. In: Danvy, O., Filinski, A. (eds) Programs as Data Objects. PADO 2001. Lecture Notes in Computer Science, vol 2053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44978-7_10

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  • DOI: https://doi.org/10.1007/3-540-44978-7_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42068-2

  • Online ISBN: 978-3-540-44978-2

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