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arXiv · 1208.3874

Upper bounds for the formula size of the majority function

Igor S. Sergeev
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Abstract

It is shown that the counting function of n Boolean variables can be implemented with the formulae of size O(n^3.06) over the basis of all 2-input Boolean functions and of size O(n^4.54) over the standard basis. The same bounds follow for the complexity of any threshold symmetric function of n variables and particularly for the majority function. Any bit of the product of binary numbers of length n can be computed by formulae of size O(n^4.06) or O(n^5.54) depending on basis. Incidentally the bounds O(n^3.23) and O(n^4.82) on the formula size of any symmetric function of n variables with respect to the basis are obtained.

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Igor S. Sergeev. 2012-08-19. Upper bounds for the formula size of the majority function. https://arxiv.org/abs/1208.3874

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