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文章基本信息

  • 标题:Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in terms of Fourier sparsity
  • 本地全文:下载
  • 作者:Swagato Sanyal
  • 期刊名称:Electronic Colloquium on Computational Complexity
  • 印刷版ISSN:1433-8092
  • 出版年度:2014
  • 卷号:2014
  • 出版社:Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
  • 摘要:

    We prove that the Fourier dimension of any Boolean function with Fourier sparsity s is at most O s log s . This bound is tight upto a factor of log s as the Fourier dimension and sparsity of the address function are quadratically related. We obtain the bound by observing that the Fourier dimension of a Boolean function is equivalent to its non-adaptive parity decision tree complexity, and then bounding the latter.

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