The Fourier Entropy-Influence Conjecture for Certain Classes of Boolean Functions
نویسندگان
چکیده
In 1996, Friedgut and Kalai made the Fourier Entropy–Influence Conjecture: For every Boolean function f : {−1, 1} → {−1, 1} it holds that H[f̂] ≤ C · I[f ], where H[f̂] 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 Sn1×· · ·×Snd where d is constant. We also verify the conjecture for functions computable by read-once decision trees. ? {odonnell,jswright,yuanzhou}@cs.cmu.edu. This research performed while the first author was a member of the School of Mathematics, Institute for Advanced Study. Supported by NSF grants CCF-0747250 and CCF-0915893, BSF grant 2008477, and Sloan and Okawa fellowships.
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