# The monotone circuit complexity of boolean functions

@article{Alon1987TheMC,
title={The monotone circuit complexity of boolean functions},
author={N. Alon and R. Boppana},
journal={Combinatorica},
year={1987},
volume={7},
pages={1-22}
}
• Published 1987
• Mathematics, Computer Science
• Combinatorica
Recently, Razborov obtained superpolynomial lower bounds for monotone circuits that cliques in graphs. In particular, Razborov showed that detecting cliques of sizes in a graphm vertices requires monotone circuits of size Ω(ms/(logm)2s) for fixeds, and sizemΩ(logm) form/4].In this paper we modify the arguments of Razborov to obtain exponential lower bounds for circuits. In particular, detecting cliques of size (1/4) (m/logm)2/3 requires monotone circuits exp (Ω((m/logm)1/3)). For fixeds, any… Expand
366 Citations

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