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International Joint Conference on Automated Reasoning

IJCAR 2014: Automated Reasoning pp 168–183Cite as

Computing All Implied Equalities via SMT-Based Partition Refinement

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

Abstract

Consequence finding is used in many applications of deduction. This paper develops and evaluates a suite of optimized SMT-based algorithms for computing equality consequences over arbitrary formulas and theories supported by SMT solvers. It is inspired by an application in the SLAyer analyzer, where our new algorithms are commonly 10–100x faster than simpler algorithms. The main idea is to incrementally refine an initially coarse partition using models extracted from a solver. Our approach requires only O(N) solver calls for N terms, but in the worst case creates O(N 2) fresh subformulas. Simpler algorithms, in contrast, require O(N 2) solver calls. We also describe an asymptotically superior algorithm that requires O(N) solver calls and only O(NlogN) fresh subformulas. We evaluate algorithms which reduce the number of fresh formulas required either by using specialized data structures or by relying on subformula sharing.

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Author information

Authors and Affiliations

  1. Microsoft Research, USA

    Josh Berdine & Nikolaj Bjørner

Authors
  1. Josh Berdine
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  2. Nikolaj Bjørner
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Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

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© 2014 Springer International Publishing Switzerland

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Berdine, J., Bjørner, N. (2014). Computing All Implied Equalities via SMT-Based Partition Refinement. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-08587-6_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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