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Effective Encodings of Constraint Programming Models to SMT

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Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

Satisfiability Modulo Theories (SMT) is a well-established methodology that generalises propositional satisfiability (SAT) by adding support for a variety of theories such as integer arithmetic and bit-vector operations. SMT solvers have made rapid progress in recent years. In part, the efficiency of modern SMT solvers derives from the use of specialised decision procedures for each theory. In this paper we explore how the Essence Prime constraint modelling language can be translated to the standard SMT-LIB language. We target four theories: bit-vectors (QF_BV), linear integer arithmetic (QF_LIA), non-linear integer arithmetic (QF_NIA), and integer difference logic (QF_IDL). The encodings are implemented in the constraint modelling tool Savile Row. In an extensive set of experiments, we compare our encodings for the four theories, showing some notable differences and complementary strengths. We also compare our new encodings to the existing work targeting SMT and SAT, and to a well-established learning CP solver. Our two proposed encodings targeting the theory of bit-vectors (QF_BV) both substantially outperform earlier work on encoding to QF_BV on a large and diverse set of problem classes.

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Notes

  1. 1.

    Experiment scripts, model and parameter files and raw results can be found at: https://github.com/stacs-cp/CP2020-SRSMT  [10].

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Acknowledgements

We thank Marc Roig Vilamala who worked on an early version of the SMT backend of Savile Row. This work is supported by EPSRC grant EP/P015638/1.

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Authors and Affiliations

  1. School of Computer Science, University of St Andrews, St Andrews, UK

    Ewan Davidson, Özgür Akgün & Joan Espasa

  2. Department of Computer Science, University of York, York, UK

    Peter Nightingale

Authors
  1. Ewan Davidson
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  2. Özgür Akgün
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  3. Joan Espasa
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  4. Peter Nightingale
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Corresponding author

Correspondence to Joan Espasa .

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Editors and Affiliations

  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Davidson, E., Akgün, Ö., Espasa, J., Nightingale, P. (2020). Effective Encodings of Constraint Programming Models to SMT. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_9

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_9

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