Languages with bounded multiparty communication complexity
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Tight bounds for monotone switching networks via fourier analysis
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We prove that a monotone circuit of size nd recognizing connectivity must have depth $\Omega((\log n)^2/\log d)$. For formulas this implies depth $\Omega((\log n)^2/\log\log n)$. For polynomial-size circuits the bound becomes $\Omega((\log n)^2)$ which is optimal up to a constant.