Interpolation Systems for Ground Proofs in Automated Deduction: a Survey

• 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((Formula presented.)) 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Inbäddad systemteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Embedded Systems (hsv//eng)

Nyckelord

Satisfiability modulo theories

Decision procedures

Theory combination

Interpolation systems

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)