A Slight Sharpening of LMN

摘要

N. Linial et al. (1993, J. Assoc. Comput. Mach.40, No. 3, 607–620) proved that a function computed by a small-depth circuit of limited size has most of its Fourier support on small sets. We improve their bounds. When the bottom fanin is bounded we use essentially their argument, but to reduce the general case to this case without a loss in the asymptotic bounds requires a new argument.