A slight sharpening of LMN
J Håstad - Journal of Computer and System Sciences, 2001 - Elsevier
Journal of Computer and System Sciences, 2001•Elsevier
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.
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.
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.
Elsevier