Interpolation and Symbol Elimination

Kovács, Laura; Воронков, Андрей

doi:10.1007/978-3-642-02959-2_17

Cited by 49 publications

(82 citation statements)

References 23 publications

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“…The interpolation theorem is frequently stated in the following form (see [18] for a discussion of the consequences of this change in formulation):…”

Section: Interpolationmentioning

confidence: 99%

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Mutual Exclusion by Interpolation

Kriener

King

2012

Functional and Logic Programming

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Abstract. The question of what constraints must hold for a predicate to behave as a (partial) function, is key to understanding the behaviour of a logic program. It has been shown how this question can be answered by combining backward analysis, a form of analysis that propagates determinacy requirements against the control flow, with a component for deriving so-called mutual exclusion conditions. The latter infers conditions sufficient to ensure that if one clause yields an answer then another cannot. This paper addresses the challenge of how to compute these conditions by showing that this problem can be reformulated as that of vertex enumeration. Whilst directly applicable in logic programming, the method might well also find application in reasoning about type classes.

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“…The interpolation theorem is frequently stated in the following form (see [18] for a discussion of the consequences of this change in formulation):…”

Section: Interpolationmentioning

confidence: 99%

“…Given two formulae A and B, such that A ∧ B |= ⊥ (their conjunct A ∧ B is infeasible), there exists a formula I, such that A |= I and I ∧ B |= ⊥ and comps(I) ⊆ comps(A) ∩ comps(B). Koács and Voronkov [18] introduce the term 'reverse interpolant' for this formula and we follow their terminology.…”

Section: Interpolationmentioning

confidence: 99%

Mutual Exclusion by Interpolation

Kriener

King

2012

Functional and Logic Programming

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“…The study of variables that can be eliminated from a formula is an issue of gaining interest [13,15]. Several researchers have noticed that an interpolant can contain fewer variables than V A,B .…”

Section: Related Workmentioning

confidence: 99%

Propositional Interpolation and Abstract Interpretation

D’Silva

2010

Programming Languages and Systems

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Abstract. Algorithms for computing Craig interpolants have several applications in program verification. Though different algorithms exist, the relationship between them and the properties of the interpolants they generate are not well understood. This paper is a study of interpolation algorithms for propositional resolution proofs. We show that existing interpolation algorithms are abstractions of a more general, parametrised algorithm. Further, existing algorithms reside in the coarsest abstraction that admits correct interpolation algorithms. The strength of interpolants constructed by existing interpolation algorithms and the variables they eliminate are analysed. The algorithms and their properties are formulated and analysed using abstract interpretation.

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“…[16]. For this reason, recent papers [5,9,11,14,18,19,21] consider the problem of obtaining small interpolants for various theories.…”

Section: Introductionmentioning

confidence: 99%

Playing in the grey area of proofs

2012

Self Cite

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Interpolation is an important technique in verification and static analysis of programs. In particular, interpolants extracted from proofs of various properties are used in invariant generation and bounded model checking. A number of recent papers studies interpolation in various theories and also extraction of smaller interpolants from proofs. In particular, there are several algorithms for extracting of interpolants from so-called local proofs. The main contribution of this paper is a technique of minimising interpolants based on transformations of what we call the "grey area" of local proofs. Another contribution is a technique of transforming, under certain common conditions, arbitrary proofs into local ones.Unlike many other interpolation techniques, our technique is very general and applies to arbitrary theories. Our approach is implemented in the theorem prover Vampire and evaluated on a large number of benchmarks coming from first-order theorem proving and bounded model checking using logic with equality, uninterpreted functions and linear integer arithmetic. Our experiments demonstrate the power of the new techniques: for example, it is not unusual that our proof transformation gives more than a tenfold reduction in the size of interpolants.

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Interpolation and Symbol Elimination

Cited by 49 publications

References 23 publications

Mutual Exclusion by Interpolation

Mutual Exclusion by Interpolation

Propositional Interpolation and Abstract Interpretation

Playing in the grey area of proofs

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