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  • 标题:Any Monotone Property of 3-uniform Hypergraphs is Weakly Evasive
  • 本地全文:下载
  • 作者:Raghav Kulkarni ; Youming Qiao ; Xiaoming Sun
  • 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:

    For a Boolean function f let D(f) denote its deterministic decision tree complexity, i.e., minimum number of (adaptive) queries required in worst case in order to determine f In a classic paper,Rivest and Vuillemin \cite{rv} show that any non-constant monotone property :012n01 of n-vertex graphs has D()=(n2)

    We extend their result to 3-uniform hypergraphs. In particular, we show that any non-constant monotone property :013n01 of n-vertex 3-uniform hypergraphs has D()=(n3)

    Our proof combines the combinatorial approach of Rivest and Vuillemin with the topological approach of Kahn, Saks, and Sturtevant. Interestingly, our proof makes use of Vinogradov's Theorem (weak Goldbach Conjecture), inspired by its recent use by Babai et. al. \cite{bbkn} in the context of the topological approach. Our work leaves the generalization to k-uniform hypergraphs as an intriguing open question.

  • 关键词:decision tree complexity; evasiveness; group actions; hypergraph properties; query complexity
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