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Function Synthesis for Maximizing Model Counting

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14499))

Abstract

Given a boolean formula \(\phi (X, Y, Z)\), the Max#SAT problem [10, 29] asks for finding a partial model on the set of variables X, maximizing its number of projected models over the set of variables Y. We investigate a strict generalization of Max#SAT allowing dependencies for variables in X, effectively turning it into a synthesis problem. We show that this new problem, called DQMax#SAT, subsumes both the DQBF [23] and DSSAT [19] problems. We provide a general resolution method, based on a reduction to Max#SAT, together with two improvements for dealing with its inherent complexity. We further discuss a concrete application of DQMax#SAT for symbolic synthesis of adaptive attackers in the field of program security. Finally, we report preliminary results obtained on the resolution of benchmark problems using a prototype DQMax#SAT solver implementation.

This work was supported by the French national projects TAVA (ANR-20-CE25-0009) and SECUREVAL (ANR-22-PECY-05).

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Notes

  1. 1.

    Actually these problems can even be reduced to SSAT instances.

  2. 2.

    Thanks to specific parametrization and the oracles [5] used internally by BaxMC, it can be considered an exact solver on the small instances of interest in this section.

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Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes) Verimag, 38000, Grenoble, France

    Thomas Vigouroux, Marius Bozga, Cristian Ene & Laurent Mounier

Authors
  1. Thomas Vigouroux
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  2. Marius Bozga
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  3. Cristian Ene
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  4. Laurent Mounier
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Correspondence to Marius Bozga .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Vigouroux, T., Bozga, M., Ene, C., Mounier, L. (2024). Function Synthesis for Maximizing Model Counting. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14499. Springer, Cham. https://doi.org/10.1007/978-3-031-50524-9_12

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  • DOI: https://doi.org/10.1007/978-3-031-50524-9_12

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  • Online ISBN: 978-3-031-50524-9

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