Proceedings of Computational Complexity. Twelfth Annual IEEE Conference (1997)

Ulm GERMANY

June 24, 1997 to June 27, 1997

ISSN: 1093-0159

ISBN: 0-8186-7907-7

pp: 297

Janos Simon , University of Chicago

Shi-Chun Tsai , National Chi-Nan International University

ABSTRACT

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.

INDEX TERMS

Monotone circuit, lower bound, approximation method, bottleneck counting method

CITATION

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.

doi:10.1109/CCC.1997.612324

CITATIONS