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Boolean functions whose monotone complexity is of size n2/log n

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Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 104))

Abstract

We construct a sequence of monotone Boolean functions hn:{0, 1}n→{0, 1}n, such that the monotone complexity of hn is of order n2/log n. This result includes the largest known lower bound of this kind. Previously there were an Ω(n3/2) bound for the Boolean matrix product, an Ω(n5/3) bound for Boolean sums and an Ω(n2/log2n) bound of the author for the same functions hn. This new lower bound is proved by new methods which probably will turn out to be useful also for other problems.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 4800, Bielefeld 1, Germany

    Ingo Wegener

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  1. Ingo Wegener
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Peter Deussen

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© 1981 Springer-Verlag Berlin Heidelberg

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Wegener, I. (1981). Boolean functions whose monotone complexity is of size n2/log n. In: Deussen, P. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017292

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  • DOI: https://doi.org/10.1007/BFb0017292

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10576-3

  • Online ISBN: 978-3-540-38561-5

  • eBook Packages: Springer Book Archive

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