A theorem on probabilistic constant depth Computations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On monotone formulae with restricted depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Exponential lower bounds for restricted monotone circuits
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Circuits and local computation
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On monotone formulae with restricted depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The complexity of computations by networks
IBM Journal of Research and Development - Mathematics and computing
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We prove an exponential lower bound for the majority function on constant depth monotone circuits, solving an open problem of A. Yao's.. In particular, we prove that computing majority on depth d monotone circuits requires exp&Ohgr;(n1/(d-1)) size. Using this result we also get exponential lower bounds for other problems, such as connectivity and cliques.