Noise Stable Halfspaces are Close to Very Small Juntas

Bourgain [Bou02] showed that any noise stable Boolean function f can be well-approximated by a junta. In this note we give an exponential sharpening of the parameters of Bourgain’s result under the additional assumption that f is a halfspace.

• Type: Journal
• Year: 2016
• Where: CJTCS
• Authors: Ilias Diakonikolas, Ragesh Jaiswal, Rocco A. Servedio, Li-Yang Tan, Andrew Wan
• Keywords: CJTCS 2016, Hardware