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Constraint solving for finite model finding in SMT solvers*

Published online by Cambridge University Press:  28 June 2017

ANDREW REYNOLDS ,
CESARE TINELLI  and
CLARK BARRETT
ANDREW REYNOLDS
Affiliation:
Department of Computer Science, The University of Iowa, Iowa City, Iowa, USA (e-mail: andrew.j.reynolds@gmail.com, cesare-tinelli@uiowa.edu)
CESARE TINELLI
Affiliation:
Department of Computer Science, The University of Iowa, Iowa City, Iowa, USA (e-mail: andrew.j.reynolds@gmail.com, cesare-tinelli@uiowa.edu)
CLARK BARRETT
Affiliation:
Department of Computer Science, Stanford University, Stanford, California, USA (e-mail: barrett@cs.stanford.edu)
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Abstract

Satisfiability modulo theories (SMT) solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing SMT solvers to report “unknown” when they fail to prove the unsatisfiability of a formula with quantifiers. This inability to return counter models limits their usefulness in applications that produce queries involving quantified formulas. In this paper, we reduce these limitations by integrating finite model finding techniques based on constraint solving into the architecture used by modern SMT solvers. This approach is made possible by a novel solver for cardinality constraints, as well as techniques for on-demand instantiation of quantified formulas. Experiments show that our approach is competitive with the state of the art in SMT, and orthogonal to approaches in automated theorem proving.

Keywords

Satisfiability modulo theoriesfinite model finding
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Issue 4 , July 2017 , pp. 516 - 558
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

*

The work of the first two authors was partially funded by a grant from Intel Corporation.

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