dc.contributor.author |
Das, Bireswar |
|
dc.contributor.author |
Pal, Manjish |
|
dc.contributor.author |
Visavaliya, Vijay |
|
dc.date.accessioned |
2014-03-24T18:31:30Z |
|
dc.date.available |
2014-03-24T18:31:30Z |
|
dc.date.issued |
2011-10 |
|
dc.identifier.citation |
Das, Bireswar; Pal, Manjish and Visavaliya, Vijay, “The entropy influence conjecture revisited”, arXiv, Cornell University Library,DOI: http://arxiv.org/abs/1110.4301, Oct. 2011. |
en_US |
dc.identifier.uri |
arXiv:1110.4301 |
|
dc.identifier.uri |
https://repository.iitgn.ac.in/handle/123456789/985 |
|
dc.description.abstract |
In this paper, we prove that most of the boolean functions, f : {−1, 1} n → {−1, 1}satisfy the Fourier Entropy Influence (FEI) Conjecture due to Friedgut and Kalai(Proc. AMS’96)[1]. The conjecture says that the Entropy of a boolean function is at most a constant times the Influence of the function. The conjecture has been proven for families of functions of smaller sizes. O’donnell, Wright and Zhou (ICALP’11)[7] verified the conjecture for the family of symmetric functions, whose size is 2n+1. They are in fact able to prove the conjecture for the family of d-part symmetric functions for constant d, the size of whose is 2O(nd). Also it is known that the conjecture is true for a large fraction of polynomial sized DNFs (COLT’10)[5]. Using elementary methods we prove that a random function with high probability satisfies the conjecture with the constant as (2 + δ), for any constant δ > 0. |
en_US |
dc.description.statementofresponsibility |
by Bireswar Das, Manjish Pal and Vijay Visavaliya |
|
dc.language.iso |
en |
en_US |
dc.publisher |
arXiv, Cornell University Library |
en_US |
dc.subject |
Combinatorics |
en_US |
dc.subject |
Computational complexity |
en_US |
dc.subject |
Discrete mathematics |
en_US |
dc.subject |
Fourier entropy influence |
en_US |
dc.title |
The Entropy Influence Conjecture Revisited |
en_US |
dc.type |
Preprint |
|