# On the sum-of-squares degree of symmetric quadratic functions

@inproceedings{Lee2016OnTS,
title={On the sum-of-squares degree of symmetric quadratic functions},
author={Troy Lee and Anupam Prakash and Ronald de Wolf and Henry S. Yuen},
booktitle={Computational Complexity Conference},
year={2016}
}
• Published in
Computational Complexity…
11 January 2016
• Mathematics, Computer Science
We study how well functions over the boolean hypercube of the form $f_k(x)=(|x|-k)(|x|-k-1)$ can be approximated by sums of squares of low-degree polynomials, obtaining good bounds for the case of approximation in $\ell_{\infty}$-norm as well as in $\ell_1$-norm. We describe three complexity-theoretic applications: (1) a proof that the recent breakthrough lower bound of Lee, Raghavendra, and Steurer on the positive semidefinite extension complexity of the correlation and TSP polytopes cannot be…
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