ABC: Algebraic Bound Computation for Loops

Blanc, Régis; Henzinger, Thomas A.; Hottelier, Thibaud; Kovács, Laura

doi:10.1007/978-3-642-17511-4_7

Cited by 43 publications

(42 citation statements)

References 16 publications

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“…Furthermore, the precision of our analysis could be improved by using ideas from control-flow refinement (as those by Flores-Montoya and Hähnle [2014]). Moreover, the techniques in the tool ABC [Blanc et al 2010] could be invoked whenever our separated analysis from Sect. 6.2 proposes a sub-program whose shape is suitable for the specialized analysis of Blanc et al [2010].…”

Section: Resultsmentioning

confidence: 99%

“…We contacted the authors of SPEED [Gulwani et al 2009], but were not able to obtain their tool. We decided not to compare KoAT to ABC [Blanc et al 2010], RAML [Hoffmann et al 2012;Hoffmann and Shao 2014], or r-TuBound [Knoop et al 2012], as their input or analysis goals differ considerably from ours. As benchmarks, we collected 689 programs from the literature on termination and complexity of integer programs.…”

Section: Discussionmentioning

confidence: 99%

“…The tool SPEED [Gulwani et al 2009] instruments programs by counters and employs an invariant generation tool to obtain bounds on these counters. The ABC system [Blanc et al 2010] also determines symbolic bounds for nested loops, but does not treat sequences of loops.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Analyzing Runtime and Size Complexity of Integer Programs

Brockschmidt

Emmes

Falke

et al. 2016

ACM Trans. Program. Lang. Syst.

135

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We present a modular approach to automatic complexity analysis of integer programs. Based on a novel alternation between finding symbolic time bounds for program parts and using these to infer bounds on the absolute values of program variables, we can restrict each analysis step to a small part of the program while maintaining a high level of precision. The bounds computed by our method are polynomial or exponential expressions that depend on the absolute values of input parameters.We show how to extend our approach to arbitrary cost measures, allowing to use our technique to find upper bounds for other expended resources, such as network requests or memory consumption. Our contributions are implemented in the open source tool KoAT, and extensive experiments show the performance and power of our implementation in comparison with other tools.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Analyzing Runtime and Size Complexity of Integer Programs

Brockschmidt

Emmes

Falke

et al. 2016

ACM Trans. Program. Lang. Syst.

135

View full text Add to dashboard Cite

show abstract

“…Blanc et al [10] and Gulwani et al [16] present algorithms to compute symbolic bounds of loop trip counts. However, the computed trip counts may not be sufficiently precise for equivalence checking proofs.…”

Section: Related Workmentioning

confidence: 99%

Automatic Equivalence Checking of UF+IA Programs

Lopes

Monteiro

2013

Model Checking Software

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Abstract. Proving the equivalence of programs has several important applications, including algorithm recognition, regression checking, compiler optimization verification, 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 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 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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“…On the other hand, our method is more general in that it does not restrict the number of loops occurring in the path pro-gram, and benefits from regarding both interpolation and transitive closure computation as black boxes. The ability to compute closed forms of certain loops is also exploited in algebraic approaches [6]. These approaches can also naturally be generalized to perform useful over-approximation [1] and under-approximation.…”

Section: Related Workmentioning

confidence: 99%

Accelerating Interpolants

Hojjat

Iosif

Konecny

et al. 2012

Automated Technology for Verification and Analysis

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Abstract. We present Counterexample-Guided Accelerated Abstraction Refinement (CEGAAR), a new algorithm for verifying infinite-state transition systems. CEGAAR combines interpolation-based predicate discovery in counterexampleguided predicate abstraction with acceleration technique for computing the transitive closure of loops. CEGAAR applies acceleration to dynamically discovered looping patterns in the unfolding of the transition system, and combines overapproximation with underapproximation. It constructs inductive invariants that rule out an infinite family of spurious counterexamples, alleviating the problem of divergence in predicate abstraction without losing its adaptive nature. We present theoretical and experimental justification for the effectiveness of CE-GAAR, showing that inductive interpolants can be computed from classical Craig interpolants and transitive closures of loops. We present an implementation of CEGAAR that verifies integer transition systems. We show that the resulting implementation robustly handles a number of difficult transition systems that cannot be handled using interpolation-based predicate abstraction or acceleration alone.

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ABC: Algebraic Bound Computation for Loops

Cited by 43 publications

References 16 publications

Analyzing Runtime and Size Complexity of Integer Programs

Analyzing Runtime and Size Complexity of Integer Programs

Automatic Equivalence Checking of UF+IA Programs

Accelerating Interpolants

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