Complexity and Limiting Ratio of Boolean Functions over Implication
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Monotone circuits for the majority function
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
The fraction of large random trees representing a given Boolean function in implicational logic
Random Structures & Algorithms
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The amplification of probabilistic Boolean formulas refers to combining independent copies of such formulas to reduce the error probability. Les Valiant used the amplification method to produce monotone Boolean formulas of size O(n5.3) for the majority function of n variables. In this paper we show that the amount of amplification that Valiant obtained is optimal. In addition, using the amplification method we give an O(k4.3 n log n) upper bound for the size of monotone formulas computing the kth threshold function of n variables.