Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

  title={Interpolation Systems for Ground Proofs in Automated Deduction: a Survey},
  author={Maria Paola Bonacina and Moa Johansson},
  journal={Journal of Automated Reasoning},
Interpolation is a deductive technique applied in program analysis and verification: for example, it is used to compute over-approximations of images or refine abstractions. An interpolation system takes a refutation and extracts an interpolant by building it inductively from partial interpolants. We survey color-based interpolation systems for ground proofs produced by key inference engines of state-of-the-art solvers: DPLL for propositional logic, equality sharing for combination of convex… 
Craig Interpolation with Clausal First-Order Tableaux
We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way
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  • Mathematics, Computer Science
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  • 2018
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Decidable fragments of first-order logic and of first-order linear arithmetic with uninterpreted predicates
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Disjunctive Interpolants for Horn-Clause Verification
A new notion of interpolation is introduced, disjunctive interpolation, which solves a more general class of problems in one step compared to previous notions of interpolant, such as tree interpolants or inductive sequences of interpolants.
Flexible interpolation with local proof transformations
This paper presents a technique for transforming the propositional proof produced by an SMT-Solver in such a way that mixed predicates are eliminated and can be applied to allow the reuse of known interpolation algorithms.
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Novel techniques for interpolation-based software model checking, an approximate method which uses Craig interpolation to compute invariants of programs and a heuristic that aims to avoid the repeated and computationally expensive construction of interpolants, thus enabling the detection of deeply buried defects such as buffer overflows.
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  • Computer Science, Mathematics
    2011 Formal Methods in Computer-Aided Design (FMCAD)
  • 2011
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