### Abstract

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.

Original language | English (US) |
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Title of host publication | Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings |

Pages | 330-341 |

Number of pages | 12 |

Edition | PART 1 |

DOIs | |

State | Published - Jul 11 2011 |

Externally published | Yes |

Event | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland Duration: Jul 4 2011 → Jul 8 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 1 |

Volume | 6755 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 38th International Colloquium on Automata, Languages and Programming, ICALP 2011 |
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Country | Switzerland |

City | Zurich |

Period | 7/4/11 → 7/8/11 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings*(PART 1 ed., pp. 330-341). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-22006-7_28

**The fourier entropy-influence conjecture for certain classes of Boolean functions.** / O'Donnell, Ryan; Wright, John; Zhou, Yuan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings.*PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6755 LNCS, pp. 330-341, 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, Zurich, Switzerland, 7/4/11. https://doi.org/10.1007/978-3-642-22006-7_28

}

TY - GEN

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

AU - O'Donnell, Ryan

AU - Wright, John

AU - Zhou, Yuan

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.

UR - http://www.scopus.com/inward/record.url?scp=79959978489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959978489&partnerID=8YFLogxK

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

ER -