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pymwp: A Static Analyzer Determining Polynomial Growth Bounds

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14216))

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Abstract

We present pymwp, a static analyzer that automatically computes, if they exist, polynomial bounds relating input and output sizes. In case of exponential growth, our tool detects precisely which dependencies between variables induced it. Based on the sound mwp-flow calculus, the analysis captures bounds on large classes of programs by being non-deterministic and not requiring termination. For this reason, implementing this calculus required solving several non-trivial implementation problems, to handle its complexity and non-determinism, but also to provide meaningful feedback to the programmer. The duality of the analysis result and compositionality of the calculus make our approach original in the landscape of complexity analyzers. We conclude by demonstrating experimentally how pymwp is a practical and performant static analyzer to automatically evaluate variable growth bounds of C programs.

This research is supported by the Transatlantic Research Partnership of the Embassy of France in the United States and the FACE Foundation, and has benefited from the research meeting 21453 “Static Analyses of Program Flows: Types and Certificate for Complexity” in Schloss Dagstuhl. Th. Rubiano and Th. Seiller are supported by the Île-de-France region through the DIM RFSI project “CoHOp”.

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Notes

  1. 1.

    Observe that the bound for X3’ involves X1 and X2: the presence of X1 in the bound of X2’ transitively impacts the bound for X3’, because the analysis is compositional.

  2. 2.

    pymwp actually outputs .

  3. 3.

    Obtaining this feedback requires to specify the --fin argument.

  4. 4.

    List of supported features: https://statycc.github.io/pymwp/features.

  5. 5.

    Full comparison: https://github.com/statycc/pymwp/compare/FSCD22...0.4.2.

  6. 6.

    A complex data structure sounds daunting, but it is in fact one of the highlights of the system, and enables to solve a difficult derivation problem efficiently. For details, see the documentation at https://statycc.github.io/pymwp/relation.

  7. 7.

    Bound of example5_1 does not appear in Table 3 because of this simplification.

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Acknowledgments

The authors wish to express their gratitude to the reviewers for their thoughtful comments, and to Antonio Flores Montoya, for the preparation and public sharing of his PhD thesis experimental evaluation resources [11].

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Authors and Affiliations

  1. School of Computer and Cyber Sciences, Augusta University, Augusta, USA

    Clément Aubert & Neea Rusch

  2. LIPN – UMR 7030 Université Sorbonne Paris Nord, Villetaneuse, France

    Thomas Rubiano & Thomas Seiller

  3. CNRS, Paris, France

    Thomas Seiller

Authors
  1. Clément Aubert
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  2. Thomas Rubiano
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  4. Thomas Seiller
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Correspondence to Clément Aubert .

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Editors and Affiliations

  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Aubert, C., Rubiano, T., Rusch, N., Seiller, T. (2023). pymwp: A Static Analyzer Determining Polynomial Growth Bounds. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14216. Springer, Cham. https://doi.org/10.1007/978-3-031-45332-8_14

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  • DOI: https://doi.org/10.1007/978-3-031-45332-8_14

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