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International Conference on Theory and Applications of Satisfiability Testing

SAT 2019: Theory and Applications of Satisfiability Testing – SAT 2019 pp 279–297Cite as

Syntax-Guided Rewrite Rule Enumeration for SMT Solvers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11628))

Abstract

The performance of modern Satisfiability Modulo Theories (SMT) solvers relies crucially on efficient decision procedures as well as static simplification techniques, which include large sets of rewrite rules. Manually discovering and implementing rewrite rules is challenging. In this work, we propose a framework that uses enumerative syntax-guided synthesis (SyGuS) to propose rewrite rules that are not implemented in a given SMT solver. We implement this framework in cvc4, a state-of-the-art SMT and SyGuS solver, and evaluate several use cases. We show that some SMT solvers miss rewriting opportunities, or worse, have bugs in their rewriters. We also show that a variation of our approach can be used to test the correctness of a rewriter. Finally, we show that rewrites discovered with this technique lead to significant improvements in cvc4 on both SMT and SyGuS problems over bit-vectors and strings.

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Notes

  1. 1.

    E.g. for checks in the theory of strings with length whose decidability is unknown [17].

  2. 2.

    For a better estimate for \(\mathsf {bvterm}_{32}\), we approximate the number as \(u_{4,n} + u_{32,n-1} - u_{4,n-1}\) where \(u_{m,n}\) is the number of unique terms for bit-width m and term size n.

  3. 3.

    The solver answered “sat”, but produced a model that did not satisfy the constraints.

  4. 4.

    The solver answered “unsat”, but accepted a model generated by cvc4 \(\mathsf {ext}\).

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Acknowledgements

This material is based upon work partially supported by the National Science Foundation (Award No. 1656926), the Office of Naval Research (Contract No. 68335-17-C-0558), and DARPA (N66001-18-C-4012, FA8650-18-2-7854 and FA8650-18-2-7861).

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Authors and Affiliations

  1. Stanford University, Stanford, USA

    Andres Nötzli, Aina Niemetz, Mathias Preiner & Clark Barrett

  2. University of Iowa, Iowa City, USA

    Andrew Reynolds, Haniel Barbosa & Cesare Tinelli

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  1. Andres Nötzli
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  2. Andrew Reynolds
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Correspondence to Andres Nötzli .

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Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Mikoláš Janota

  2. University of Lisbon, Lisbon, Portugal

    Inês Lynce

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Nötzli, A. et al. (2019). Syntax-Guided Rewrite Rule Enumeration for SMT Solvers. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-24258-9_20

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