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Annual Asian Computing Science Conference

ASIAN 1996: Concurrency and Parallelism, Programming, Networking, and Security pp 116–128Cite as

Sets as anti-chains

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1179))

Abstract

In this paper we present a theory of anti-chains as data representations for sets in circumstances where sets of interest satisfy properties such as being upward-closed or convex relative to a partial ordering. Our goal is to provide an interface for supplying an implementation of the necessary primitives in a reusable manner and a theory that will facilitate algebraic reasoning about correctness. We present an algebra of anti-chains and illustrate its use in programming and reasoning about a machine learning algorithm.

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References

  1. B. A. Davey and H. A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990.

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Author information

Authors and Affiliations

  1. University of Pennsylvania, USA

    Carl A. Gunter

  2. National University of Singapore, Singapore

    Teow-Hin Ngair

  3. Rice University, USA

    Devika Subramanian

Authors
  1. Carl A. Gunter
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  2. Teow-Hin Ngair
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  3. Devika Subramanian
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Editor information

Joxan Jaffar Roland H. C. Yap

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© 1996 Springer-Verlag Berlin Heidelberg

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Gunter, C.A., Ngair, TH., Subramanian, D. (1996). Sets as anti-chains. In: Jaffar, J., Yap, R.H.C. (eds) Concurrency and Parallelism, Programming, Networking, and Security. ASIAN 1996. Lecture Notes in Computer Science, vol 1179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027785

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  • DOI: https://doi.org/10.1007/BFb0027785

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62031-0

  • Online ISBN: 978-3-540-49626-7

  • eBook Packages: Springer Book Archive

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