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

• Main Authors: de Wolf, Ronald, Yuen, Henry, Lee, Troy, Prakash, Anupam
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2018
• Subjects: Sum-of-squares Degree; Approximation Theory; DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/90218; http://hdl.handle.net/10220/47238
• Institution: Nanyang Technological University

We study how well functions over the boolean hypercube of the form f_k(x)=(lxl-k)(lxl-k-1) can be approximated by sums of squares of low-degree polynomials, obtaining good bounds for the case of approximation in l_{infinity}-norm as well as in l_1-norm. We describe three complexity-theoretic applica...