TY - GEN

T1 - The fourier entropy-influence conjecture for certain classes of Boolean functions

AU - O'Donnell, Ryan

AU - Wright, John

AU - Zhou, Yuan

N1 - Funding Information:
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.

PY - 2011/7/11

Y1 - 2011/7/11

N2 - In 1996, Friedgut and Kalai made the Fourier Entropy- Influence Conjecture: For every Boolean function it holds that , where 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 where d is constant. We also verify the conjecture for functions computable by read-once decision trees.

AB - In 1996, Friedgut and Kalai made the Fourier Entropy- Influence Conjecture: For every Boolean function it holds that , where 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 where d is constant. We also verify the conjecture for functions computable by read-once decision trees.

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U2 - 10.1007/978-3-642-22006-7_28

DO - 10.1007/978-3-642-22006-7_28

M3 - Conference contribution

AN - SCOPUS:79959978489

SN - 9783642220050

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 330

EP - 341

BT - Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings

T2 - 38th International Colloquium on Automata, Languages and Programming, ICALP 2011

Y2 - 4 July 2011 through 8 July 2011

ER -