On the Spectral Properties of Symmetric Functions
Computational Complexity
2017-04-12 v1 Functional Analysis
Abstract
We characterize the approximate monomial complexity, sign monomial complexity , and the approximate L 1 norm of symmetric functions in terms of simple combinatorial measures of the functions. Our characterization of the approximate L 1 norm solves the main conjecture in [AFH12]. As an application of the characterization of the sign monomial complexity, we prove a conjecture in [ZS09] and provide a characterization for the unbounded-error communication complexity of symmetric-xor functions.
Keywords
Cite
@article{arxiv.1704.03176,
title = {On the Spectral Properties of Symmetric Functions},
author = {Anil Ada and Omar Fawzi and Raghav Kulkarni},
journal= {arXiv preprint arXiv:1704.03176},
year = {2017}
}