Abstraction Refinement for Quantified Array Assertions

Seghir, Mohamed Nassim; Podelski, Andreas; Wies, Thomas

doi:10.1007/978-3-642-03237-0_3

Cited by 33 publications

(29 citation statements)

References 33 publications

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“…Effectiveness and performances of abstraction/refinement approaches strongly depend on their ability in generating the "right" predicates to stop divergence of verification procedures. In case of programs with arrays, this quest can rely on ghost variables [21] retrieved from the post-conditions, on the backward propagation of post-conditions along spurious counterexamples [33] or can be constraint-based [9,34]. Recently, constraint-based techniques have been significantly extended to the generation of loop invariants outside the array property fragment [29].…”

Section: Introductionmentioning

confidence: 99%

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Definability of Accelerated Relations in a Theory of Arrays and Its Applications

Alberti

Ghilardi

Sharygina

2013

Frontiers of Combining Systems

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Abstraction (in its various forms) is a powerful established technique in modelchecking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an approach which is widely used to avoid divergence, but it has been applied mostly to integer programs. This paper addresses the problem of accelerating transition relations for unbounded arrays with the ultimate goal of avoiding divergence during reachability analysis of abstract programs. For this, we first design a format to compute accelerations in this domain; then we show how to adapt the so-called 'monotonic abstraction' technique to efficiently handle complex formulae with nested quantifiers generated by the acceleration preprocessing. Notably, our technique can be easily plugged-in into abstraction/refinement loops, and strongly contributes to avoid divergence: experiments conducted with the MCMT model checker attest the effectiveness of our approach on programs with unbounded arrays, where acceleration and abstraction/refinement technologies fail if applied alone.

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Section: Introductionmentioning

confidence: 99%

“…For example, predicate abstraction approaches (i.e., [3,4,33]) fail verifying the procedures in Figure1, which are commonly considered to be challenging for verifiers because they cause divergence 3 . Acceleration, on the other side, provides a precise and systematic way for addressing the verification of programs.…”

Section: Introductionmentioning

confidence: 99%

Definability of Accelerated Relations in a Theory of Arrays and Its Applications

Alberti

Ghilardi

Sharygina

2013

Frontiers of Combining Systems

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“…In [21,34] a predicate abstraction for inferring universally quantified properties of array elements is presented, and in [26] the authors present a similar technique which uses template-based quantified abstract domains. In [46] a backward reachability analysis based on predicate abstraction and abstraction refinement is used for verifying assertions which are universally quantified over array indexes.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Program Verification using Constraint Handling Rules and Array Constraint Generalizations*

Angelis

Fioravanti

Pettorossi

et al. 2017

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Abstract. The transformation of constraint logic programs (CLP programs) has been shown to be an effective methodology for verifying properties of imperative programs. By following this methodology, we encode the negation of a partial correctness property of an imperative program prog as a predicate incorrect defined by a CLP program P , and we show that prog is correct by transforming P into the empty program through the application of semantics preserving transformation rules. Some of these rules perform replacements of constraints that encode properties of the data structures manipulated by the program prog. In this paper we show that Constraint Handling Rules (CHR) are a suitable formalism for representing and applying constraint replacements during the transformation of CLP programs. In particular, we consider programs that manipulate integer arrays and we present a CHR encoding of a constraint replacement strategy based on the theory of arrays. We also propose a novel generalization strategy for constraints on integer arrays that combines the CHR constraint replacement strategy with various generalization operators for linear constraints, such as widening and convex hull. Generalization is controlled by additional constraints that relate the variable identifiers in the imperative program prog and the CLP representation of their values. The method presented in this paper has been implemented and we have demonstrated its effectiveness on a set of benchmark programs taken from the literature.

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“…Furthermore, their method is based on the use of monotonic changes to the array (which is not the case for Loop 1) and it requires a pre-analysis of indexes (causing an extra slow-down). The techniques of Jhala and McMillan [20,30] and of Seghir, Podelski and Wies [35] make use of the loop postconditions to be proven in order to infer the quantified loop invariants. Suppose we remove (**) and (***) from the example.…”

Section: Under-approximations and Templatesmentioning

confidence: 99%

A parametric segmentation functor for fully automatic and scalable array content analysis

Cousot

Logozzo

2011

Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Abstraction Refinement for Quantified Array Assertions

Cited by 33 publications

References 33 publications

Definability of Accelerated Relations in a Theory of Arrays and Its Applications

Definability of Accelerated Relations in a Theory of Arrays and Its Applications

Program Verification using Constraint Handling Rules and Array Constraint Generalizations*

A parametric segmentation functor for fully automatic and scalable array content analysis

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