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SMT Sampling via Model-Guided Approximation

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Formal Methods (FM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14000))

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Abstract

We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in model checking and formal verification, this aspect is relatively under-explored. Prior work exists for generating such assignments, or samples, for Boolean formulas and for quantifier-free first-order formulas involving bit-vectors, arrays, and uninterpreted functions (QF_AUFBV). We propose a new approach that is suitable for a theory T of integer arithmetic and to T with arrays and uninterpreted functions. The approach involves reducing the general sampling problem to a simpler instance of sampling from a set of independent intervals, which can be done efficiently. Such reduction is carried out by expanding a single model—a seed—using top-down propagation of constraints along the original first-order formula.

This work is supported by the Israeli Science Foundation Grant No. 243/19 and the Binational Science Foundation (NSF-BSF) Grant No. 2018675.

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Notes

  1. 1.

    Available at: https://github.com/chaosite/MeGASampler.

  2. 2.

    The arity of functions is restricted to 1 for simplicity of presentation; an extension of our algorithm to functions with arbitrary arity is straightforward.

  3. 3.

    The “interesting” operation in \(T_{\text {NIA}}\) is multiplication; most benchmarks in this directory are actually in \(T_{\text {MIA}}\), which is supported by MeGASampler.

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Acknowledgements

The authors would like to thank Profs. Orna Grumberg and Ofer Strichman for their valuable input and contributions to this work. We would additionally like to thank the anonymous reviewers for their time and effort.

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Authors and Affiliations

  1. Technion—Israel Institute of Technology, Haifa, Israel

    Matan I. Peled, Bat-Chen Rothenberg & Shachar Itzhaky

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  1. Matan I. Peled
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Correspondence to Bat-Chen Rothenberg .

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  1. University of Toronto, Toronto, ON, Canada

    Marsha Chechik

  2. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  3. University of Lübeck, Lübeck, Germany

    Martin Leucker

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Peled, M.I., Rothenberg, BC., Itzhaky, S. (2023). SMT Sampling via Model-Guided Approximation. In: Chechik, M., Katoen, JP., Leucker, M. (eds) Formal Methods. FM 2023. Lecture Notes in Computer Science, vol 14000. Springer, Cham. https://doi.org/10.1007/978-3-031-27481-7_6

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