Proof Tree Preserving Tree Interpolation

Christ, Jürgen; Hoenicke, Jochen

doi:10.1007/s10817-016-9365-5

Cited by 15 publications

(22 citation statements)

References 42 publications

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“…The proof tree preserving interpolation scheme presented by Christ et al [13] allows to compute interpolants for an unsatisfiable formula using a resolution proof that is unaware of the interpolation problem.…”

Section: Proof Tree Preserving Interpolationmentioning

confidence: 99%

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Efficient Interpolation for the Theory of Arrays

Hoenicke

Schindler

2018

Lecture Notes in Computer Science

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Existing techniques for Craig interpolation for the quantifierfree fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning (A, B) of the interpolation problem to avoid creating AB-mixed terms. We present a new approach using Proof Tree Preserving Interpolation and an array solver based on Weak Equivalence on Arrays. We give an interpolation algorithm for the lemmas produced by the array solver. The computed interpolants have worst-case exponential size for extensionality lemmas and worst-case quadratic size otherwise. We show that these bounds are strict in the sense that there are lemmas with no smaller interpolants. We implemented the algorithm and show that the produced interpolants are useful to prove memory safety for C programs.

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Section: Proof Tree Preserving Interpolationmentioning

confidence: 99%

“…Thus, when computing sequence [23] or tree interpolants [19], they would require either an adapted interpolation procedure or the solver has to run multiple times. In contrast, our method can easily be extended to tree interpolation [11].…”

Section: Introductionmentioning

confidence: 99%

Efficient Interpolation for the Theory of Arrays

Hoenicke

Schindler

2018

Lecture Notes in Computer Science

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“…To prove program properties over a combination of data structures, such as integers, arrays and pointers, several approaches based on theory-specific reasoning have been proposed, see e.g. [14,5,4]. While powerful, these techniques are limited to quantifier-free fragments of first-order logic.…”

Section: Introductionmentioning

confidence: 99%

Splitting Proofs for Interpolation

Gleiss

Kovács

Suda

2017

Automated Deduction – CADE 26

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We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the common signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refutation into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.

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“…Most of the interpolation-based verification methods, for example [16,5,7,22,4], require explicit construction of local proofs in the combined quantifier-free theory of linear arithmetic with uninterpreted function symbols. While local proofs in such proof systems can always be found, the construction of local proofs is theory specific, and thus cannot be easily extended to other theories, especially those with quantifiers.…”

Section: Related Workmentioning

confidence: 99%

“…Some of the interpolation-based verification methods compute interpolants from proofs by restricting proofs to so-called local (or split) proofs [14,15]. In particular, [16,7,22,4] apply theory-specific transformations and generate quantifier-free interpolants from local SMT proofs in various theories, whereas [17,15] build quantified interpolants from local proofs in full first-order logic.…”

Section: Introductionmentioning

confidence: 99%

First-Order Interpolation and Interpolating Proof Systems

Kovács

Воронков

EPiC Series in Computing

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It is known that one can extract Craig interpolants from so-called local derivations. An interpolant extracted from such a derivation is a boolean combination of formulas occurring in the derivation. However, standard complete proof systems, such as superposition, for theories having the interpolation property are not necessarily complete for local proofs.In this paper we investigate interpolant extraction from non-local refutations (proofs of contradiction) in the superposition calculus and prove a number of general results about interpolant extraction and complexity of extracted interpolants. In particular, we prove that the number of quantifier alternations in first-order interpolants of formulas without quantifier alternations is unbounded. The proof of this result relies on a small number of assumptions about the theory and the proof system, so it also applies to many first-order theories beyond predicate logic. This result has far-reaching consequences for using local proofs as a foundation for interpolating proof systems -any such proof system should deal with formulas of arbitrary quantifier complexity.To search for alternatives for interpolating proof systems, we consider several variations on interpolation and local proofs. Namely, we give an algorithm for building interpolants from resolution refutations in logic without equality and discuss additional constraints when this approach can be also used for logic with equality. We finally propose a new direction related to interpolation via local proofs in first-order theories.

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Proof Tree Preserving Tree Interpolation

Cited by 15 publications

References 42 publications

Efficient Interpolation for the Theory of Arrays

Efficient Interpolation for the Theory of Arrays

Splitting Proofs for Interpolation

First-Order Interpolation and Interpolating Proof Systems

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