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Program Sketching Using Lifted Analysis for Numerical Program Families

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NASA Formal Methods (NFM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12673))

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Abstract

This work presents a novel approach for synthesizing numerical program sketches using lifted (family-based) static program analysis. In particular, our approach leverages a lifted static analysis based on abstract interpretation, which is used for analyzing program families with numerical features. It takes as input the common code base, which encodes all variants of a program family, and produces precise results for all variants in a single analysis run. The elements of the underlying lifted analysis domain are decision trees, in which decision nodes are labeled with linear constraints defined over numerical features and leaf nodes belong to a given single-program analysis domain.

We encode a program sketch as a program family such that holes correspond to numerical features and all possible sketch realizations correspond to variants in the program family. Then, we preform a lifted analysis of the family, so that only those variants that satisfy all assertions under all possible inputs represent correct realizations of holes in the sketch.

We have implemented an experimental program synthesizer for resolving C sketches. It is based on a lifted static analyzer for \(\texttt {\#if}\)-based C program families, which uses the numerical domains from the APRON  library. An evaluation yields promising results. Moreover, our approach provides speedups in some cases against the popular sketching tool Sketch  and can solve some numerical benchmarks that Sketch  cannot handle.

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Notes

  1. 1.

    This is only high-level description of the encoding. For the precise definition, we refer to Sect. 3.3. See the HelloWorld  program family in Fig. 5a.

  2. 2.

    Since any \(k \in \mathbb {K}\) is a valuation function, we have that either \(k \models \theta \) holds or \(k \not \models \theta \) (which is equivalent to \(k \models \lnot \theta \)) holds, for any \(\theta \in \textit{FeatExp}(\mathbb {F})\).

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Authors and Affiliations

  1. Mother Teresa University, St. Mirche Acev nr. 4, 1000, Skopje, North Macedonia

    Aleksandar S. Dimovski

  2. Saarland University, Saarland Informatics Campus, E1.1, 66123, Saarbrücken, Germany

    Sven Apel

  3. Université catholique de Louvain, 1348, Ottignies-Louvain-la-Neuve, Belgium

    Axel Legay

Authors
  1. Aleksandar S. Dimovski
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  2. Sven Apel
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  3. Axel Legay
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Corresponding author

Correspondence to Aleksandar S. Dimovski .

Editor information

Editors and Affiliations

  1. NASA Langley Research Center, Hampton, VA, USA

    Aaron Dutle

  2. National Institute of Aerospace, Hampton, VA, USA

    Mariano M. Moscato

  3. National Institute of Aerospace, Hampton, VA, USA

    Laura Titolo

  4. NASA Langley Research Center, Hampton, VA, USA

    César A. Muñoz

  5. National Institute of Aerospace, Hampton, VA, USA

    Ivan Perez

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Dimovski, A.S., Apel, S., Legay, A. (2021). Program Sketching Using Lifted Analysis for Numerical Program Families. In: Dutle, A., Moscato, M.M., Titolo, L., Muñoz, C.A., Perez, I. (eds) NASA Formal Methods. NFM 2021. Lecture Notes in Computer Science(), vol 12673. Springer, Cham. https://doi.org/10.1007/978-3-030-76384-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-76384-8_7

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