Automatically Refining Abstract Interpretations

Gulavani, Bhargav S.; Chakraborty, Supratik; Nori, Aditya V.; Rajamani, Sriram K.

doi:10.1007/978-3-540-78800-3_33

Cited by 75 publications

(62 citation statements)

References 24 publications

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“…The benchmark popl07 is the program in Fig. 1 and the motivating example of [4]; cav06 and tacas08 are the motivating examples from [21] and [22] respectively. The next four benchmarks are programs from the test suite of InvGen.…”

Section: Methodsmentioning

confidence: 99%

“…These approaches include (i) template-based techniques, such as [26,6,27], (ii) techniques based on predicate abstraction such as [11,12,13,22,5], and (iii) techniques based on probabilistic inference [4]. While some of these approaches are, in principle, capable of discovering precise invariants in loops exhibiting multiple phases, they are significantly more complicated, less efficient, and less widely-used than standard abstract interpretation-based techniques for generating conjunctive numeric invariants such as [1,2,28].…”

Section: Related Workmentioning

confidence: 99%

“…However, these techniques often diverge or take a very large number of refinement steps. More sophisticated invariant generation techniques based on predicate abstraction are considered in [13,22,5]. The basic idea underlying [13] is to use interpolants to generate counterexamples.…”

Section: Related Workmentioning

confidence: 99%

“…Hence, a poor choice of language degrades its performance. The technique described in [22] uses counterexample guided abstraction refinement to tune widening strategies in an abstract interpretation framework. While this technique can sometimes be helpful for generating more precise invariants for multi-phase loops, it is difficult to characterize the class of loops for which this technique will generate useful invariants.…”

Section: Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Simplifying Loop Invariant Generation Using Splitter Predicates

Sharma

Dillig

et al. 2011

Computer Aided Verification

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Abstract. We present a novel static analysis technique that substantially improves the quality of invariants inferred by standard loop invariant generation techniques. Our technique decomposes multi-phase loops, which require disjunctive invariants, into a semantically equivalent sequence of single-phase loops, each of which requires simple, conjunctive invariants. We define splitter predicates which are used to identify phase transitions in loops, and we present an algorithm to find useful splitter predicates that enable the phase-reducing transformation. We show experimentally on a set of representative benchmarks from the literature and real code examples that our technique substantially increases the quality of invariants inferred by standard invariant generation techniques. Our technique is conceptually simple, easy to implement, and can be integrated into any automatic loop invariant generator.

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Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Simplifying Loop Invariant Generation Using Splitter Predicates

Sharma

Dillig

et al. 2011

Computer Aided Verification

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“…Predicate abstraction based tools are geared towards computing arbitrary boolean combinations of predicates [6,9,31,1,10,30]. Among these, Yogi [31] uses test cases to determine where to refine its abstraction.…”

Section: Comparison With Linear Invariant Generationmentioning

confidence: 99%

Verification as Learning Geometric Concepts

et al. 2013

Self Cite

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Abstract. We formalize the problem of program verification as a learning problem, showing that invariants in program verification can be regarded as geometric concepts in machine learning. Safety properties define bad states: states a program should not reach. Program verification explains why a program's set of reachable states is disjoint from the set of bad states. In Hoare Logic, these explanations are predicates that form inductive assertions. Using samples for reachable and bad states and by applying well known machine learning algorithms for classification, we are able to generate inductive assertions. By relaxing the search for an exact proof to classifiers, we obtain complexity theoretic improvements. Further, we extend the learning algorithm to obtain a sound procedure that can generate proofs containing invariants that are arbitrary boolean combinations of polynomial inequalities. We have evaluated our approach on a number of challenging benchmarks and the results are promising.

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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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Automatically Refining Abstract Interpretations

Cited by 75 publications

References 24 publications

Simplifying Loop Invariant Generation Using Splitter Predicates

Simplifying Loop Invariant Generation Using Splitter Predicates

Verification as Learning Geometric Concepts

NIL: Learning Nonlinear Interpolants

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