Noise Stable Halfspaces are Close to Very Small Juntas.

Chicago J. Theor. Comput. Sci.(2016)

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摘要
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.
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