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Quantifier-free interpolation in combinations of equality interpolating theories

Published: 06 March 2014 Publication History

Abstract

The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly reuse interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the strong (sub-)amalgamation property. Then, we provide an equivalent syntactic characterization and show that such characterization covers most theories commonly employed in verification. Finally, we design a combined quantifier-free interpolation algorithm capable of handling both convex and nonconvex theories; this algorithm subsumes and extends most existing work on combined interpolation.

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    cover image ACM Transactions on Computational Logic
    ACM Transactions on Computational Logic  Volume 15, Issue 1
    February 2014
    279 pages
    ISSN:1529-3785
    EISSN:1557-945X
    DOI:10.1145/2590829
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 06 March 2014
    Accepted: 01 May 2013
    Received: 01 December 2012
    Published in TOCL Volume 15, Issue 1

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    Author Tags

    1. Combined interpolation
    2. Craig interpolation theorem
    3. satisfiability modulo theories
    4. strong amalgamability

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    • (2022)Interpolation and Uniform Interpolation in Quantifier-Free Fragments of Combined First-Order TheoriesMathematics10.3390/math1003046110:3(461)Online publication date: 31-Jan-2022
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