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)


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.


Boolean Function Symmetric Function Fourier Spectrum Logarithmic Sobolev Inequality Annual IEEE Symposium 
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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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