Satisfiability of Non-linear (Ir)rational Arithmetic

  • Harald Zankl
  • Aart Middeldorp
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

non-linear arithmetic SMT solving term rewriting termination matrix interpretations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Harald Zankl
    • 1
  • Aart Middeldorp
    • 1
  1. 1.Institute of Computer ScienceUniversity of InnsbruckAustria

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