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Disjunctive Interval Analysis

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Static Analysis (SAS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12913))

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Abstract

We revisit disjunctive interval analysis based on the Boxes abstract domain. We propose the use of what we call range decision diagrams (RDDs) to implement Boxes, and we provide algorithms for the necessary RDD operations. RDDs tend to be more compact than the linear decision diagrams (LDDs) that have traditionally been used for Boxes. Representing information more directly, RDDs also allow for the implementation of more accurate abstract operations. This comes at no cost in terms of analysis efficiency, whether LDDs utilise dynamic variable ordering or not. RDD and LDD implementations are available in the Crab analyzer, and our experiments confirm that RDDs are well suited for disjunctive interval analysis.

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Notes

  1. 1.

    With a little additional effort, the approach extends to rationals and floating point numbers.

  2. 2.

    Gurfinkel and Chaki [11] consider a restricted programming language with only linear expressions and guards.

  3. 3.

    It is straightforward to translate an RDD to an LDD over bounds constraints, and vice versa.

  4. 4.

    This view explains our tendency to use notation like [3, 4) for what is obviously a (closed) singleton integer interval.

  5. 5.

    As presented, this differs slightly from [11] in that we select the left sibling as replacement in widen-edge, where [11] selects the right. We also implemented a right-biased variant, and differences are minimal.

  6. 6.

    Available at https://github.com/seahorn/crab.

  7. 7.

    Available at https://github.com/seahorn/clam.

  8. 8.

    Available at https://github.com/seahorn/ldd.

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Acknowledgements

We thank the three anonymous reviewers for their careful reading of an earlier version of the paper, and their constructive suggestions for how to improve it. Jorge Navas has been supported by the National Science Foundation under grant number 1816936.

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Authors and Affiliations

  1. Faculty of Information Technology, Monash University, Melbourne, Australia

    Graeme Gange & Peter J. Stuckey

  2. SRI International, Menlo Park, CA, USA

    Jorge A. Navas

  3. School of Computing and Information Systems, The University of Melbourne, Melbourne, Australia

    Peter Schachte & Harald Søndergaard

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  1. Graeme Gange
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  2. Jorge A. Navas
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  4. Harald Søndergaard
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Correspondence to Harald Søndergaard .

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Editors and Affiliations

  1. Informal Systems, Inria, ENS, DI - Ecole Normale Supérieure, Paris, France

    Cezara Drăgoi

  2. Microsoft Corporation, Redmond, WA, USA

    Suvam Mukherjee

  3. Nokia Bell Labs, Murray Hill, NJ, USA

    Kedar Namjoshi

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Gange, G., Navas, J.A., Schachte, P., Søndergaard, H., Stuckey, P.J. (2021). Disjunctive Interval Analysis. In: Drăgoi, C., Mukherjee, S., Namjoshi, K. (eds) Static Analysis. SAS 2021. Lecture Notes in Computer Science(), vol 12913. Springer, Cham. https://doi.org/10.1007/978-3-030-88806-0_7

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