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Designing Theory Solvers with Extensions

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Book cover Frontiers of Combining Systems (FroCoS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10483))

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Abstract

Satisfiability Modulo Theories (SMT) solvers have been developed to natively support a wide range of theories, including linear arithmetic, bit-vectors, strings, algebraic datatypes and finite sets. They handle constraints in these theories using specialized theory solvers. In this paper, we overview the design of these solvers, specifically focusing on theories whose function symbols are partitioned into a base signature and an extended signature. We introduce generic techniques that can be used in solvers for extended theories, including a new context-dependent simplification technique and model-based refinement techniques. We provide case studies showing our techniques can be leveraged for reasoning in an extended theory of strings, for bit-vector approaches that rely on lazy bit-blasting and for new approaches to non-linear arithmetic.

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Notes

  1. 1.

    See [34] for more details.

  2. 2.

    For details on our experiments, see http://cvc4.stanford.edu/papers/ FroCoS2017-ext.

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Acknowledgments

We would like to thank Liana Hadarean and Martin Brain for helpful discussion about bit-vectors, and Tim King for his support for arithmetic in cvc4.

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Authors and Affiliations

  1. Department of Computer Science, The University of Iowa, Iowa, USA

    Andrew Reynolds, Cesare Tinelli & Dejan Jovanović

  2. Department of Computer Science, Stanford University, Stanford, USA

    Clark Barrett

  3. SRI International, Menlo Park, USA

    Dejan Jovanović

Authors
  1. Andrew Reynolds
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  2. Cesare Tinelli
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  3. Dejan Jovanović
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  4. Clark Barrett
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Corresponding author

Correspondence to Cesare Tinelli .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Clare Dixon

  2. University of Sao Paulo, Sao Paulo, Brazil

    Marcelo Finger

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Reynolds, A., Tinelli, C., Jovanović, D., Barrett, C. (2017). Designing Theory Solvers with Extensions. In: Dixon, C., Finger, M. (eds) Frontiers of Combining Systems. FroCoS 2017. Lecture Notes in Computer Science(), vol 10483. Springer, Cham. https://doi.org/10.1007/978-3-319-66167-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-66167-4_2

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