# Exponential lower bounds for restricted monotone circuits

@article{Valiant1983ExponentialLB, title={Exponential lower bounds for restricted monotone circuits}, author={Leslie G. Valiant}, journal={Proceedings of the fifteenth annual ACM symposium on Theory of computing}, year={1983} }

In this paper we consider monotone Boolean circuits with three alternations, in the order “or”, “and”, “or.” Whenever the number of alternations is limited to a fixed constant the formula and circuit size measures are polynomially related to each other. We shall therefore refer to this measure interchangeably as ΣπΣ-formula size or ΣπΣ-circuit size. We shall prove that any such circuit or formula for detecting the existence of cliques in an N-node graph has at least 2Ω(Nε) gates for some ε > 0… Expand

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