Abstract
Craig’s interpolation theorem has numerous applications in model checking, automated reasoning, and synthesis. There is a variety of interpolation systems which derive interpolants from refutation proofs; these systems are ad-hoc and rigid in the sense that they provide exactly one interpolant for a given proof. In previous work, we introduced a parametrised interpolation system which subsumes existing interpolation methods for propositional resolution proofs and enables the systematic variation of the logical strength and the elimination of non-essential variables in interpolants. In this paper, we generalise this system to propositional hyper-resolution proofs as well as clausal proofs. The latter are generated by contemporary SAT solvers. Finally, we show that, when applied to local (or split) proofs, our extension generalises two existing interpolation systems for first-order logic and relates them in logical strength.
Highlights
Craig interpolation [14] has proven to be an effective heuristic in applications such as model checking, where it is used as an approximate method for computing invariants of transition systems [39,54], and synthesis, where interpolants represent deterministic implementations of specifications given as relations [31]
– We generalise our interpolation system for hyper-resolution steps to clausal refutations generated by contemporary SAT solvers such as PicoSAT [5], allowing us to avoid the generation of intermediate interpolants
We focus on interpolation systems that construct an interpolant from an (A, B)-refutation by mapping the vertices of a resolution proof to a formula called the partial interpolant
Summary
Craig interpolation [14] has proven to be an effective heuristic in applications such as model checking, where it is used as an approximate method for computing invariants of transition systems [39,54], and synthesis, where interpolants represent deterministic implementations of specifications given as relations [31]. The intrinsic properties of interpolants enable concise abstractions in verification and smaller circuits in synthesis. Interpolation is mostly treated as a black box, leaving no room for a systematic exploration of the solution space. The use of different interpolation systems complicates a comparison of their interpolants. We present a novel framework which generalises a number of existing interpolation techniques and supports a systematic variation and comparison of the generated interpolants
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