On the bottleneck counting argument

Both the bottleneck counting argument 7, 8] and Razborov's approximation method 1, 4, 12] 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.