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International Conference on Verification, Model Checking, and Abstract Interpretation

VMCAI 2016: Verification, Model Checking, and Abstract Interpretation pp 185–205Cite as

\(D^3\): Data-Driven Disjunctive Abstraction

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

Abstract

We address the problem of computing an abstraction for a set of examples, which is precise enough to separate them from a set of counterexamples. The challenge is to find an over-approximation of the positive examples that does not represent any negative example. Conjunctive abstractions (e.g., convex numerical domains) and limited disjunctive abstractions, are often insufficient, as even the best such abstraction might include negative examples. One way to improve precision is to consider a general disjunctive abstraction.

We present \(D^3\), a new algorithm for learning general disjunctive abstractions. Our algorithm is inspired by widely used machine-learning algorithms for obtaining a classifier from positive and negative examples. In contrast to these algorithms which cannot generalize from disjunctions, \(D^3\) obtains a disjunctive abstraction that minimizes the number of disjunctions. The result generalizes the positive examples as much as possible without representing any of the negative examples. We demonstrate the value of our algorithm by applying it to the problem of data-driven differential analysis, computing the abstract semantic difference between two programs. Our evaluation shows that \(D^3\) can be used to effectively learn precise differences between programs even when the difference requires a disjunctive representation.

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Notes

  1. 1.

    A most specific representation need not exist. For simplicity of the presentation, we consider the case where it does, and explain what adaptations are needed when it does not.

  2. 2.

    If \(\beta \) maps a concrete point to a single concept which best represents it, it is easily shown that it suffices to maintain S as a single element. Candidate Elimination can also handle multiple representations, in which case S will be a set of specific bounds, similarly to G.

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Acknowledgment

The research leading to these results has received funding from the European Union’s - Seventh Framework Programme (FP7) under grant agreement no. 615688 - ERC-COG-PRIME and under ERC grant agreement no. 321174-VSSC, and from the BSF grant no. 2012259.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Hila Peleg & Eran Yahav

  2. The Academic College of Tel Aviv-Yaffo, Tel Aviv, Israel

    Sharon Shoham

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  1. Hila Peleg
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  2. Sharon Shoham
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  3. Eran Yahav
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Correspondence to Hila Peleg .

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Editors and Affiliations

  1. EPFL IC-DO, Lausanne, Switzerland

    Barbara Jobstmann

  2. Microsoft Research, Redmond, Washington, USA

    K. Rustan M. Leino

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Peleg, H., Shoham, S., Yahav, E. (2016). \(D^3\): Data-Driven Disjunctive Abstraction. 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_9

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  • DOI: https://doi.org/10.1007/978-3-662-49122-5_9

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