Year: 2018
Type: conference-paper
Abstract: In 1991, Craig Gotsman and Nathan Linial conjectured that for all n and d, the average sensitivity of a degree-d polynomial threshold function on n variables is maximized by the degree-d symmetric polynomial which computes the parity function on the d layers of the hypercube with Hamming weight closest to n/2. We refute the conjecture for almost all d and for almost all n, and we confirm the conjecture in many of the remaining cases.
Author: Brynmor Chapman
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2779077750