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Satisfiability of Non-linear (Ir)rational Arithmetic

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6355))

Abstract

We present a novel way for reasoning about (possibly ir)rational quantifier-free non-linear arithmetic by a reduction to SAT/SMT. The approach is incomplete and dedicated to satisfiable instances only but is able to produce models for satisfiable problems quickly. These characteristics suffice for applications such as termination analysis of rewrite systems. Our prototype implementation, called MiniSmt, is made freely available. Extensive experiments show that it outperforms current SMT solvers especially on rational and irrational domains.

This research is supported by FWF (Austrian Science Fund) project P18763.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Harald Zankl & Aart Middeldorp

Authors
  1. Harald Zankl
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  2. Aart Middeldorp
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Editor information

Editors and Affiliations

  1. Carnegie Mellon University, USA

    Edmund M. Clarke

  2. School of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Zankl, H., Middeldorp, A. (2010). Satisfiability of Non-linear (Ir)rational Arithmetic. In: Clarke, E.M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science(), vol 6355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17511-4_27

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  • DOI: https://doi.org/10.1007/978-3-642-17511-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17510-7

  • Online ISBN: 978-3-642-17511-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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