Journal of Automated Reasoning

, Volume 54, Issue 4, pp 353–390 | Cite as

Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

Article

Abstract

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 theories, and DPLL(\(\mathcal {T}\)) for SMT-solving. Since color-based interpolation systems use colors to track symbols in proofs, equality is problematic, because replacement of equals by equals mixes symbols and therefore colors. We analyze interpolation in the presence of equality, and we demonstrate the color-based approach by giving a complete interpolation system for ground proofs by superposition.

Keywords

Interpolation systems Satisfiability modulo theories Decision procedures Theory combination 

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Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di VeronaVeronaItaly
  2. 2.Department of Computer ScienceChalmers University of TechnologyGöteborgSweden

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