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Efficient E-Matching for SMT Solvers

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Book cover Automated Deduction – CADE-21 (CADE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4603))

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Abstract

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to instantiate quantified variables. This paper introduces algorithms that identify matches on E-graphs incrementally and efficiently. In particular, we introduce an index that works on E-graphs, called E-matching code trees that combine features of substitution and code trees, used in saturation based theorem provers. E-matching code trees allow performing matching against several patterns simultaneously. The code trees are combined with an additional index, called the inverted path index, which filters E-graph terms that may potentially match patterns when the E-graph is updated. Experimental results show substantial performance improvements over existing state-of-the-art SMT solvers.

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Authors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA, 98074, USA

    Leonardo de Moura & Nikolaj Bjørner

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  1. Leonardo de Moura
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  2. Nikolaj Bjørner
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Frank Pfenning

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© 2007 Springer-Verlag Berlin Heidelberg

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de Moura, L., Bjørner, N. (2007). Efficient E-Matching for SMT Solvers. In: Pfenning, F. (eds) Automated Deduction – CADE-21. CADE 2007. Lecture Notes in Computer Science(), vol 4603. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73595-3_13

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  • DOI: https://doi.org/10.1007/978-3-540-73595-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73594-6

  • Online ISBN: 978-3-540-73595-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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