research-article

Efficient generation of craig interpolants in satisfiability modulo theories

Authors:

Alessandro Cimatti,

Alberto Griggio,

Roberto SebastianiAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 12, Issue 1

Article No.: 7, Pages 1 - 54

https://doi.org/10.1145/1838552.1838559

Published: 26 November 2010 Publication History

Abstract

The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of efficient generation of interpolants for some important fragments of first-order logic, which are amenable for effective decision procedures, called satisfiability 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 define a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach.

Efficiency is ensured by the fact that the proposed interpolation algorithms extend state-of-the-art algorithms for satisfiability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.

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Cited By

Redondi GCimatti AGriggio AMcmillan K(2024)Invariant Checking for SMT-Based Systems with QuantifiersACM Transactions on Computational Logic10.1145/368615325:4(1-37)Online publication date: 3-Aug-2024
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Cimatti AGriggio AMover SRoveri MTonetta S(2023)Verification modulo theoriesFormal Methods in System Design10.1007/s10703-023-00434-x60:3(452-481)Online publication date: 19-Sep-2023
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Blicha MHyvärinen AKofroň JSharygina N(2022)Using linear algebra in decomposition of Farkas interpolantsInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-021-00641-z24:1(111-125)Online publication date: 1-Feb-2022
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Index Terms

Efficient generation of craig interpolants in satisfiability modulo theories
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Models of computation
    1. Computability

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 12, Issue 1

October 2010

334 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1838552

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Copyright © 2010 ACM.

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Publication History

Published: 26 November 2010

Accepted: 01 December 2009

Received: 01 June 2009

Published in TOCL Volume 12, Issue 1

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Cimatti AGriggio AMover SRoveri MTonetta S(2023)Verification modulo theoriesFormal Methods in System Design10.1007/s10703-023-00434-x60:3(452-481)Online publication date: 19-Sep-2023
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Blicha MHyvärinen AKofroň JSharygina N(2022)Using linear algebra in decomposition of Farkas interpolantsInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-021-00641-z24:1(111-125)Online publication date: 1-Feb-2022
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Blicha MFedyukovich GHyvärinen ASharygina N(2022)Transition Power Abstractions for Deep Counterexample DetectionTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-030-99524-9_29(524-542)Online publication date: 30-Mar-2022
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