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Quantitative abstraction refinement

Published:23 January 2013Publication History
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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.

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  1. Quantitative abstraction refinement

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            • Published in

              cover image ACM SIGPLAN Notices
              ACM SIGPLAN Notices  Volume 48, Issue 1
              POPL '13
              January 2013
              561 pages
              ISSN:0362-1340
              EISSN:1558-1160
              DOI:10.1145/2480359
              Issue’s Table of Contents
              • cover image ACM Conferences
                POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
                January 2013
                586 pages
                ISBN:9781450318327
                DOI:10.1145/2429069

              Copyright © 2013 ACM

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              Association for Computing Machinery

              New York, NY, United States

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              • Published: 23 January 2013

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