Higher lower bounds on monotone size
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Finite Limits and Monotone Computations: The Lower Bounds Criterion
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
General Pseudo-random Generators from Weaker Models of Computation
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the monotone circuit complexity of quadratic boolean functions
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices. For 5/spl les/s/spl les/m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2) 1.8/sup min(/spl radic/s-1/2,m/(4s))/ gates. If a non-monotone circuit computes CLIQUE using a "small" amount of negation, then the circuit contains an exponential number of gates. The former is proved very simply using so called bottleneck counting argument within the framework of approximation, whereas the latter is verified introducing a notion of restricting negation and generalizing the sunflower contraction.