Predicate Generation for Learning-Based Quantifier-Free Loop Invariant Inference

Jung, Young-Seok; Lee, Wonchan; Wang, Bow-Yaw; Yi, Kwangkuen

doi:10.1007/978-3-642-19835-9_17

Cited by 11 publications

(11 citation statements)

References 18 publications

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“…While in [14,15,16], how to apply the local property of Craig interpolants generated from a counter-example to refine the abstract model in order to exclude the spurious counter-example in CEGAR was investigated. Meanwhile, in [17], using interpolation technique to generate a set of atomic predicates as the base of machine-learning based verification technique was investigated by Wang et al…”

Section: Introductionmentioning

confidence: 99%

Generating Non-linear Interpolants by Semidefinite Programming

Dai

Xia

Zhan

2013

Computer Aided Verification

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Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model checking, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Note that δ 1 can be represented as 923.42(0.90 + 0.7y − 0.1y + 0.43x ) 2 + 252.84(0.42 − 0.28y + 0.21y − 0.84x ) 2 + 461.69(−0.1 − 0.83y + 0.44y + 0.34x ) 2 + 478(−0.06 + 0.48y + 0.87y +0.03x ) 2 +578.94(x) 2 . Similarly, δ 2 and δ 3 can be represented as sums of squares also.Moreover, using the approach in [25], we can prove θ is an inductive invariant of the loop, therefore, error() will never be executed.

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Section: Introductionmentioning

confidence: 99%

Generating Non-linear Interpolants by Semidefinite Programming

Dai

Xia

Zhan

2013

Computer Aided Verification

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“…Inferring unknown targets over fixed variables however is not realistic in applications such as loop invariant generation [11,14,12], or contextual assumption synthesis [5,4]. In loop invariant generation, one considers a loop annotated with pre-and post-conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The instance space hence consists of quantifier-free formulae over a given set of atomic predicates. We are interested in finding a quantifier-free formula which establishes the pre-and post-conditions in the specified instance space [11,14,12]. Note that the given set of atomic predicates may not be able to express any loop invariant.…”

Section: Introductionmentioning

confidence: 99%

“…To attest the performance of our incremental learning algorithms for Boolean functions, we compare with the classical algorithm in the learning-based loop invariant generation framework [11,14,12]. To evaluate the performance of incremental learning in typical settings, we consider a simple heuristic variable ordering from the application domain.…”

Section: Introductionmentioning

confidence: 99%

“…It is not applicable to scenarios where unknown targets are over indefinitely many variables. Combining with predicate abstraction and decision procedures, the CDNF algorithm is used to generate invariants for annotated loops [11,14,12], and transition invariants for termination analysis [16]. The classical algorithm is also deployed in assume-guarantee reasoning to infer contextual assumptions automatically [5,4].…”

Section: Introductionmentioning

confidence: 99%

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Learning Boolean Functions Incrementally

Chen

Wang

2012

Computer Aided Verification

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Classical learning algorithms for Boolean functions assume that unknown targets are Boolean functions over fixed variables. The assumption precludes scenarios where indefinitely many variables are needed. It also induces unnecessary queries when many variables are redundant. Based on a classical learning algorithm for Boolean functions, we develop two learning algorithms to infer Boolean functions over enlarging sets of ordered variables. We evaluate their performance in the learning-based loop invariant generation framework.

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NIL: Learning Nonlinear Interpolants

Chen

Wang

et al. 2019

Lecture Notes in Computer Science

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Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and existing methods have limitations on the form of formulae to be interpolated. We leverage classification techniques with space transformations and kernel tricks as established in the realm of machine learning, and present a counterexample-guided method named NIL for synthesizing polynomial interpolants, thereby yielding a unified framework tackling the interpolation problem for the general quantifier-free theory of nonlinear arithmetic, possibly involving transcendental functions. We prove the soundness of NIL and propose sufficient conditions under which NIL is guaranteed to converge, i.e., the derived sequence of candidate interpolants converges to an actual interpolant, and is complete, namely the algorithm terminates by producing an interpolant if there exists one. The applicability and effectiveness of our technique are demonstrated experimentally on a collection of representative benchmarks from the literature, where in particular, our method suffices to address more interpolation tasks, including those with perturbations in parameters, and in many cases synthesizes simpler interpolants compared with existing approaches.Interpolation-based technique provides a powerful mechanism for local and modular reasoning, thereby improving scalability of various verification techniques, e.g., theorem proving, model checking and abstract interpretation, to name just a few. The study of interpolation was pioneered by Krajíček [26] and Pudlák [34] in connection with theorem proving, by McMillan [29] in the context of model checking, by Graf and Saïdi [16], McMillan [30] and Henzinger et al. [19] pertaining to abstraction like CE-GAR [7], and by Wang et al. [23] in the context of learning-based invariant generation.

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Predicate Generation for Learning-Based Quantifier-Free Loop Invariant Inference

Cited by 11 publications

References 18 publications

Generating Non-linear Interpolants by Semidefinite Programming

Generating Non-linear Interpolants by Semidefinite Programming

Learning Boolean Functions Incrementally

NIL: Learning Nonlinear Interpolants

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