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Efficient generation of craig interpolants in satisfiability modulo theories

Efficient generation of craig interpolants in satisfiability modulo theories Ef cient Generation of Craig Interpolants in Satis ability Modulo Theories ALESSANDRO CIMATTI FBK-IRST and ALBERTO GRIGGIO and ROBERTO SEBASTIANI Universita di Trento ` The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of ef cient generation of interpolants for some important fragments of rst-order logic, which are amenable for effective decision procedures, called satis ability modulo theory (SMT) solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we de ne a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach. Ef ciency is ensured by the fact that the proposed interpolation algorithms extend state-ofthe-art algorithms for satis ability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more ef ciently than other competitor solvers. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic ”Mechanical theorem proving General Terms: Theory, Algorithms Additional Key Words and Phrases: Craig http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Efficient generation of craig interpolants in satisfiability modulo theories

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2010 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/1838552.1838559
Publisher site
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Abstract

Ef cient Generation of Craig Interpolants in Satis ability Modulo Theories ALESSANDRO CIMATTI FBK-IRST and ALBERTO GRIGGIO and ROBERTO SEBASTIANI Universita di Trento ` The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of ef cient generation of interpolants for some important fragments of rst-order logic, which are amenable for effective decision procedures, called satis ability modulo theory (SMT) solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we de ne a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach. Ef ciency is ensured by the fact that the proposed interpolation algorithms extend state-ofthe-art algorithms for satis ability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more ef ciently than other competitor solvers. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic ”Mechanical theorem proving General Terms: Theory, Algorithms Additional Key Words and Phrases: Craig

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Oct 1, 2010

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