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Symmetric functions in AC 0 can be computed in constant depth with very small size

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Mathematical Foundations of Computer Science 1990 (MFCS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 452))

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Abstract

It is well-known which symmetric Boolean functions can be computed by constant depth, polynomial size, unbounded fan-in circuits, i.e. which are contained in the complexity class AC 0. This result is sharpened. Symmetric Boolean functions in AC 0 can be computed by unbounded fan-in circuits with small constant depth, an almost linear number of n logO(1) n wires and a subpolynomial (but superpolylogarithmic) number of 2O(logδ n) gates for some δ<1.

Supported in part by DFG grants No. We 1066/2-1 and Me 872/1-2

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Author information

Authors and Affiliations

  1. FB Informatik, LS II, Univ. Dortmund, Postfach 500 500, 4600, Dortmund 50, Fed. Rep. of Germany

    Ingo Wegener, Norbert Wurm & Sang-Zin Yi

Authors
  1. Ingo Wegener
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  2. Norbert Wurm
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  3. Sang-Zin Yi
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Editor information

Branislav Rovan

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© 1990 Springer-Verlag Berlin Heidelberg

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Wegener, I., Wurm, N., Yi, SZ. (1990). Symmetric functions in AC 0 can be computed in constant depth with very small size. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029651

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  • DOI: https://doi.org/10.1007/BFb0029651

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52953-8

  • Online ISBN: 978-3-540-47185-1

  • eBook Packages: Springer Book Archive

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