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The Essence of Computation pp 245–265Cite as

Structure-Preserving Binary Relations for Program Abstraction

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2566))

Abstract

An abstraction is a property-preserving contraction of a program’s model into a smaller one that is suitable for automated analysis. An abstraction must be sound, and ideally, complete. Soundness and completeness arguments are intimately connected to the abstraction process, and approaches based on homomorphisms and Galois connections are commonly employed to define abstractions and prove their soundness and completeness. This paper develops Mycroft and Jones’s proprosal that an abstraction should be stated as a form of structure-preserving binary relation. Mycroft-Jones-style relations are defined, developed, and employed in characterizations of the homomorphism and Galois-connection approaches to abstraction.

Supported by NSF CCR-9970679, INT-9981558, ITR-0085949, and ITR-0086154.

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Author information

Authors and Affiliations

  1. Computing and Information Sciences Department, Kansas State University, 66506, Manhattan, KS, USA

    David A. Schmidt

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  1. David A. Schmidt
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Editor information

Editors and Affiliations

  1. DIKU, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Torben Æ. Mogensen

  2. Department of Computing and Information Sciences, Kansas State University, 234 Nichols Hall, 66506, Manhattan, KS, USA

    David A. Schmidt

  3. Department of Computer Science, University of Texas at Dallas, P.O. Box 830688, 75083, Richardson, TX, USA

    I. Hal Sudborough

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Schmidt, D.A. (2002). Structure-Preserving Binary Relations for Program Abstraction. In: Mogensen, T.Æ., Schmidt, D.A., Sudborough, I.H. (eds) The Essence of Computation. Lecture Notes in Computer Science, vol 2566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36377-7_12

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  • DOI: https://doi.org/10.1007/3-540-36377-7_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00326-7

  • Online ISBN: 978-3-540-36377-4

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