Coset decision trees and the Fourier algebra
Classical Analysis and ODEs
2019-11-11 v2 Combinatorics
Abstract
We show that if G is a finite group and f is a {0,1}-valued function on G with Fourier algebra norm at most M then f may be computed by a coset decision tree (that is a decision tree in which at each vertex we query membership of a given coset) having at most \exp(\exp(\exp(O(M^2)))) leaves. A short calculation shows that any {0,1}-valued function which may be computed by a coset decision tree with m leaves has Fourier algebra norm at most \exp(O(m)).
Cite
@article{arxiv.1805.02168,
title = {Coset decision trees and the Fourier algebra},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:1805.02168},
year = {2019}
}
Comments
28pp; corrections and typos