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Relational Constraint Solving in SMT

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

Relational logic is useful for reasoning about computational problems with relational structures, including high-level system design, architectural configurations of network systems, ontologies, and verification of programs with linked data structures. We present a modular extension of an earlier calculus for the theory of finite sets to a theory of finite relations with such operations as transpose, product, join, and transitive closure. We implement this extension as a theory solver of the SMT solver CVC4. Combining this new solver with the finite model finding features of CVC4 enables several compelling use cases. For instance, native support for relations enables a natural mapping from Alloy, a declarative modeling language based on first-order relational logic, to SMT constraints. It also enables a natural encoding of several description logics with concrete domains, allowing the use of an SMT solver to analyze, for instance, Web Ontology Language (OWL) models. We provide an initial evaluation of our solver on a number of Alloy and OWL models which shows promising results.

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Notes

  1. 1.

    A further extension of the theory to cardinality constraints is planned for future work.

  2. 2.

    Note that this theory has all the function symbols of \({\varSigma _{R}}\), not just the tuple constructors \(\langle \_, \ldots , \_\rangle \). The extra symbols are treated as uninterpreted.

  3. 3.

    All proofs of the propositions below can be found in a longer version of this paper available at http://cvc4.cs.stanford.edu/papers/CADE2017-relations/.

  4. 4.

    The Alloy Analyzer currently has built-in support for bounded integers. Any other data types need to be axiomatized in the specification.

  5. 5.

    The translation is sound only if all Alloy signatures are assumed to be finite. A full account of the translation and a proof of its soundness are beyond the scope of this paper.

  6. 6.

    Free constants have the same effect as free variables for satisfiability purposes.

  7. 7.

    Some of those domains in OWL correspond to built-in sorts in cvc4. A full translation from OWL concrete domains to cvc4 built-in sorts is beyond the scope of this work.

  8. 8.

    Detailed results and all benchmarks are available at http://cvc4.cs.stanford.edu/papers/CADE2017-relations/.

  9. 9.

    See https://www.w3.org/community/owled/ore-2015-workshop/competition.

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Acknowledgements

This work was partially supported by NSF grant no. 1228765 and by a gift from GE Global Research. We are grateful to Jasmin Blanchette and the anonymous reviewers for their very detailed comments and questions which helped improve the presentation of the paper.

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Authors and Affiliations

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

    Baoluo Meng, Andrew Reynolds & Cesare Tinelli

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

    Clark Barrett

Authors
  1. Baoluo Meng
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  2. Andrew Reynolds
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  3. Cesare Tinelli
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  4. Clark Barrett
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Corresponding author

Correspondence to Andrew Reynolds .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Meng, B., Reynolds, A., Tinelli, C., Barrett, C. (2017). Relational Constraint Solving in SMT. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_10

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_10

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