Tight bounds for monotone switching networks via fourier analysis

Authors:
Siu Man Chan;Aaron Potechin
Affiliations:
UC Berkeley, Berkeley, CA, USA;MIT, Cambridge, MA, USA
Venue:
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Year:
2012

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Abstract

We prove tight size bounds on monotone switching networks for the k-clique problem, and for an explicit monotone problem by analyzing the generation problem with a pyramid structure of height h. This gives alternative proofs of the separations of m-NC from m-P and of m-NCi from m-NCi+1, different from Raz-McKenzie (Combinatorica '99). The enumerative-combinatorial and Fourier analytic techniques in this work are very different from a large body of work on circuit depth lower bounds, and may be of independent interest.