Satisfiability of non-linear (Ir)rational arithmetic

Authors:
Harald Zankl;Aart Middeldorp
Affiliations:
Institute of Computer Science, University of Innsbruck, Austria;Institute of Computer Science, University of Innsbruck, Austria
Venue:
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Year:
2010

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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 producemodels 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.