Quantitative abstraction refinement

P. Cerny, T.A. Henzinger, A. Radhakrishna, in:, Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Language, ACM, 2013, pp. 115–128.

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Conference Paper | Published | English
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Abstract
We propose a general framework for abstraction with respect to quantitative properties, such as worst-case execution time, or power consumption. Our framework provides a systematic way for counter-example guided abstraction refinement for quantitative properties. The salient aspect of the framework is that it allows anytime verification, that is, verification algorithms that can be stopped at any time (for example, due to exhaustion of memory), and report approximations that improve monotonically when the algorithms are given more time. We instantiate the framework with a number of quantitative abstractions and refinement schemes, which differ in terms of how much quantitative information they keep from the original system. We introduce both state-based and trace-based quantitative abstractions, and we describe conditions that define classes of quantitative properties for which the abstractions provide over-approximations. We give algorithms for evaluating the quantitative properties on the abstract systems. We present algorithms for counter-example based refinements for quantitative properties for both state-based and segment-based abstractions. We perform a case study on worst-case execution time of executables to evaluate the anytime verification aspect and the quantitative abstractions we proposed.
Publishing Year
Date Published
2013-01-01
Proceedings Title
Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language
Page
115 - 128
Conference
POPL: Principles of Programming Languages
Conference Location
Rome, Italy
Conference Date
2013-07-23 – 2013-01-25
IST-REx-ID

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Cerny P, Henzinger TA, Radhakrishna A. Quantitative abstraction refinement. In: Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Language. ACM; 2013:115-128. doi:10.1145/2429069.2429085
Cerny, P., Henzinger, T. A., & Radhakrishna, A. (2013). Quantitative abstraction refinement. In Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language (pp. 115–128). Rome, Italy: ACM. https://doi.org/10.1145/2429069.2429085
Cerny, Pavol, Thomas A Henzinger, and Arjun Radhakrishna. “Quantitative Abstraction Refinement.” In Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Language, 115–28. ACM, 2013. https://doi.org/10.1145/2429069.2429085.
P. Cerny, T. A. Henzinger, and A. Radhakrishna, “Quantitative abstraction refinement,” in Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language, Rome, Italy, 2013, pp. 115–128.
Cerny P, Henzinger TA, Radhakrishna A. 2013. Quantitative abstraction refinement. Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming language. POPL: Principles of Programming Languages 115–128.
Cerny, Pavol, et al. “Quantitative Abstraction Refinement.” Proceedings of the 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Language, ACM, 2013, pp. 115–28, doi:10.1145/2429069.2429085.

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