English

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}
}