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Automating Abstract Interpretation

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9583))

Abstract

Abstract interpretation has a reputation of being a kind of “black art,” and consequently difficult to work with. This paper describes a twenty-year quest by the first author to address this issue by raising the level of automation in abstract interpretation. The most recent leg of this journey is the subject of the second author’s 2014 Ph.D. dissertation. The paper discusses several different approaches to creating correct-by-construction analyzers. Our research has allowed us to establish connections between this problem and several other areas of computer science, including automated reasoning/decision procedures, concept learning, and constraint programming.

Portions of this work appeared in [26, 35, 45, 63, 64, 66, 70, 76, 78, 81, 82]. T. Reps has an ownership interest in GrammaTech, Inc., which has licensed elements of the technology reported in this publication.

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Notes

  1. 1.

    It is interesting to note that the roles of steps (i), (iii), and (iv) are close to the steps of splitting, propagation, and join, respectively, in our generalization of St\(\mathring{\text {a}}\)lmarck’s algorithm to perform symbolic abstraction [82]. See Sect. 5.

  2. 2.

    A slight modification to the bilateral algorithm can remove the requirement of having no infinite descending chains [78].

  3. 3.

    (i) The correctness theorem for \({ focus}\) [70, Lemmas 6.8 and 6.9]; (ii) the Embedding Theorem [70, Theorem 4.9]; (iii) the correctness theorem for the finite-differencing scheme for maintaining instrumentation relations [63, Theorem 5.3]; and (iv) the correctness theorem for \({ coerce}\) [70, Theorem 6.28].

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Acknowledgments

T. Reps would like to thank the many people with whom he collaborated on the work described in the paper (as well as work that motivated the work described): for shape analysis: M. Sagiv, R. Wilhelm, a long list of their former students, as well as his own former students A. Loginov and D. Gopan; for machine-code analysis: G. Balakrishnan, J. Lim, Z. Xu, B. Miller, D. Gopan, A. Thakur, E. Driscoll, A. Lal, M. Elder, T. Sharma, and researchers at GrammaTech, Inc.; for symbolic abstraction: M. Sagiv, G. Yorsh, A. Thakur, M. Elder, T. Sharma, J. Breck, and A. Miné.

The work has been supported for many years by grants and contracts from NSF, DARPA, ONR, ARL, AFOSR, HSARPA, and GrammaTech, Inc. Special thanks go to R. Wachter, F. Anger, T. Teitelbaum and A. White.

Current support comes from a gift from Rajiv and Ritu Batra; DARPA under cooperative agreement HR0011-12-2-0012; AFRL under DARPA MUSE award FA8750-14-2-0270 and DARPA STAC award FA8750-15-C-0082; and the UW-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from WARF. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors, and do not necessarily reflect the views of the sponsoring organizations.

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  1. University of Wisconsin, Madison, WI, USA

    Thomas Reps

  2. GrammaTech, Inc., Ithaca, NY, USA

    Thomas Reps

  3. Google, Inc., Mountain View, CA, USA

    Aditya Thakur

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  1. EPFL IC-DO, Lausanne, Switzerland

    Barbara Jobstmann

  2. Microsoft Research, Redmond, Washington, USA

    K. Rustan M. Leino

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Reps, T., Thakur, A. (2016). Automating Abstract Interpretation. In: Jobstmann, B., Leino, K. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2016. Lecture Notes in Computer Science(), vol 9583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49122-5_1

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