Constraint Solving for Interpolation

Rybalchenko, Andrey; Sofronie-Stokkermans, Viorica

doi:10.1007/978-3-540-69738-1_25

Cited by 77 publications

(66 citation statements)

References 31 publications

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“…Beyer et al [11] present an algorithm to synthesize loop invariants over the UF+LIA theory, and Rybalchenko and Sofronie-Stokkermans [61] present an algorithm to synthesize interpolants over the same theory. McMillan [50] introduced an algorithm to generate interpolants from the unsatisfiability proofs of the Z3 SMT solver [22].…”

Section: Software Verification and Invariant Synthesismentioning

confidence: 99%

Automatic equivalence checking of programs with uninterpreted functions and integer arithmetic

Lopes

Monteiro

2015

Int J Softw Tools Technol Transfer

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Proving equivalence of programs has several important applications, including algorithm recognition, regression checking, compiler optimization verification and validation, and information flow checking. Despite being a topic with so many important applications, program equivalence checking has seen little advances over the past decades due to its inherent (high) complexity. In this paper, we propose, to the best of our knowledge, the first semi-algorithm for the automatic verification of partial equivalence of two programs over the combined theory of uninterpreted function symbols and integer arithmetic (UF+IA). The proposed algorithm supports, in particular, programs with nested loops. The crux of the technique is a transformation of uninterpreted functions (UFs) applications into integer polynomials, which enables the precise summarization of loops with UF applications using recurrences. The equivalence checking algorithm then proceeds on loop-free, integer only programs. We implemented the proposed technique in CORK, a tool that automatically verifies the correctness of compiler optimizations, and we show that it can prove more optimizations correct than state-of-the-art techniques.

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Section: Software Verification and Invariant Synthesismentioning

confidence: 99%

Automatic equivalence checking of programs with uninterpreted functions and integer arithmetic

Lopes

Monteiro

2015

Int J Softw Tools Technol Transfer

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“…Algorithm CI(T 1 , T 2 ) paves the way to reuse quantifier-free interpolation algorithms for both conjunctions (see, e.g., [Rybalchenko and Sofronie-Stokkermans 2010]) or arbitrary Boolean combinations of literals (see, e.g., [Cimatti et al 2008]). In particular, the capability of reusing interpolation algorithms that can efficiently handle the Boolean structure of formulae seems to be key to enlarge the scope of applicability of verification methods based on interpolants [McMillan 2011].…”

Section: A Quantifier-free Interpolating Algorithmmentioning

confidence: 99%

Quantifier-free interpolation in combinations of equality interpolating theories

Bruttomesso

Ghilardi

Ranise

2014

ACM Trans. Comput. Logic

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The use of interpolants in verification is gaining more and more importance. Since theories used in applications are usually obtained as (disjoint) combinations of simpler theories, it is important to modularly reuse interpolation algorithms for the component theories. We show that a sufficient and necessary condition to do this for quantifier-free interpolation is that the component theories have the strong (sub-)amalgamation property. Then, we provide an equivalent syntactic characterization and show that such characterization covers most theories commonly employed in verification. Finally, we design a combined quantifier-free interpolation algorithm capable of handling both convex and nonconvex theories; this algorithm subsumes and extends most existing work on combined interpolation.

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“…A natural requirement k∈b t γ k > 0 for that purpose does not allow encoding to an SDP constraint so we do not use it. Our relaxation from k∈b t γ k > 0 to k∈b t γ k ≥ 1 is inspired by [31]; it does not lead to loss of generality in our current task of finding polynomial certificates.…”

Section: Interpolation Via Positivstellensatz Sharpenedmentioning

confidence: 99%

Sharper and Simpler Nonlinear Interpolants for Program Verification

Okudono

Nishida

Kojima

et al. 2017

Programming Languages and Systems

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Abstract. Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al. that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples.

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Constraint Solving for Interpolation

Cited by 77 publications

References 31 publications

Automatic equivalence checking of programs with uninterpreted functions and integer arithmetic

Automatic equivalence checking of programs with uninterpreted functions and integer arithmetic

Quantifier-free interpolation in combinations of equality interpolating theories

Sharper and Simpler Nonlinear Interpolants for Program Verification

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