Abstract
We prove that the complexity of the implementation of the counting function of n Boolean variables by binary formulas is at most n3.03, and it is at most n4.47 for DeMorgan formulas. Hence, the same bounds are valid for the formula size of any threshold symmetric function of n variables, particularly, for the majority function. The following bounds are proved for the formula size of any symmetric Boolean function of n variables: n3.04 for binary formulas and n4.48 for DeMorgan ones. The proof is based on the modular arithmetic.
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