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}
}
  • L. Valiant
  • Published 1983
  • Computer Science, Mathematics
  • Proceedings of the fifteenth annual ACM symposium on Theory of computing
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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