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  • 标题:Decision Trees and Influence: an Inductive Proof of the OSSS Inequality
  • 本地全文:下载
  • 作者:Homin K. Lee
  • 期刊名称:Theory of Computing
  • 印刷版ISSN:1557-2862
  • 电子版ISSN:1557-2862
  • 出版年度:2010
  • 卷号:6
  • 页码:81-84
  • DOI:10.4086/toc.2010.v006a004
  • 语种:English
  • 出版社:University of Chicago
  • 摘要:We give a simple proof of the OSSS inequality (O’Donnell, Saks, Schramm, Servedio, FOCS 2005). The inequality states that for any decision tree $T$ calculating a Boolean function $f:\zo^n\rightarrow \oo$, we have $\Var[f] \leq \sum_i \delta_i(T)\Inf_i(f)$, where $\delta_i(T)$ is the probability that the input variable $x_i$ is read by $T$ and $\Inf_i(f)$ is the influence of the $i$th variable on $f$.
  • 关键词:probability; computational complexity; decision trees
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