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Partial Completeness of Abstract Fixpoint Checking

Invited Paper

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Abstraction, Reformulation, and Approximation (SARA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1864))

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Abstract

Abstract interpretation is used in program static analysis and model checking to cope with infinite state spaces and/or with computer resource limitations. One common problem is to check abstract fixpoints for specifications. The abstraction is partially complete when the checking algorithm is exact in that, if the algorithm ever terminates, its answer is always affirmative for correct specifications. We characterize partially complete abstractions for various abstract fixpoint checking algorithms, including new ones, and show that the computation of complete abstract domains is essentially equivalent to invariance proofs that is to concrete fixpoint checking.

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Author information

Authors and Affiliations

  1. Département d’informatique, École normale supérieure, 45 rue d’Ulm, 75230, Paris cedex 05, France

    Patrick Cousot

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  1. Patrick Cousot
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nebraska - Lincoln, 115 Ferguson Hall, Lincoln, NE, 68588-0115

    Berthe Y. Choueiry

  2. Department of Computer Science, University of York, Heslington, York, Y010 5DD, UK

    Toby Walsh

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Cousot, P. (2000). Partial Completeness of Abstract Fixpoint Checking. In: Choueiry, B.Y., Walsh, T. (eds) Abstraction, Reformulation, and Approximation. SARA 2000. Lecture Notes in Computer Science(), vol 1864. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44914-0_1

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  • DOI: https://doi.org/10.1007/3-540-44914-0_1

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  • Print ISBN: 978-3-540-67839-7

  • Online ISBN: 978-3-540-44914-0

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