Proceedings of Computational Complexity. Twelfth Annual IEEE Conference (1997)
June 24, 1997 to June 27, 1997
Janos Simon , University of Chicago
Shi-Chun Tsai , National Chi-Nan International University
Both Haken's bottleneck counting argument and Razborov's approximation method have been used to prove exponential lower bounds for monotone circuits. We show that under the monotone circuit model for every proof by the approximation method, there is a bottleneck counting proof and vice versa. We also illustrate the elegance of the bottleneck counting technique with a simple self-explained example: the proof of a (previously known) lower bound for the 3-CLIQUE_n problem by the bottleneck counting argument.
Monotone circuit, lower bound, approximation method, bottleneck counting method
S. Tsai and J. Simon, "A Note on the Bottleneck Counting Argument," Proceedings of Computational Complexity. Twelfth Annual IEEE Conference(CCC), Ulm GERMANY, 1997, pp. 297.