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The Fourier Entropy–Influence Conjecture for Certain Classes of Boolean Functions

  • Ryan O’Donnell
  • John Wright
  • Yuan Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

In 1996, Friedgut and Kalai made the Fourier Entropy– Influence Conjecture: For every Boolean function \(f : \{-1, 1\}^{n} \longrightarrow \{-1, 1\}\) it holds that \(H[{\widehat{f}}^{2}] \leq C \cdot I[f]\), where \(H[{\widehat{f}}^{2}]\) is the spectral entropy of f, I[f] is the total influence of f, and C is a universal constant. In this work we verify the conjecture for symmetric functions. More generally, we verify it for functions with symmetry group \(S_{n_1} \times \cdots \times S_{n_d}\) where d is constant. We also verify the conjecture for functions computable by read-once decision trees.

Keywords

Boolean Function Symmetric Function Fourier Spectrum Logarithmic Sobolev Inequality Annual IEEE Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ryan O’Donnell
    • 1
  • John Wright
    • 1
  • Yuan Zhou
    • 1
  1. 1.Department of Computer ScienceCarnegie Mellon UniversityUSA

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