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On monotone formulae with restricted depth
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Rounds in communication complexity revisited
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Resiliency of interactive distributed tasks (extended abstracts)
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We prove that every monotone circuit which tests st-connectivity of an undirected graph on n nodes has depth &OHgr;(log2n). This implies a superpolynomial (n&OHgr;(log n)) lower bound on the size of any monotone formula for st-connectivity.The proof draws intuition from a new characterization of circuit depth in terms of communication complexity. It uses counting arguments and Extremal Set Theory.Within the same framework, we also give a very simple and intuitive proof of a depth analogue of a theorem of Krapchenko concerning formula size lower bounds.