Complexity and Depth of Formulas for Symmetric Boolean Functions / *I. S. Sergeev.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 3. P. 53-57
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 127-130].

A new approach for implementation of the counting function for a Boolean set is proposed.
The approach is based on approximate calculation of sums. Using this approach,
new upper bounds for the size and depth of symmetric functions over the basis *n*-bit} binary numbers is asymptotically estimated
from above by

*Key words*:
Boolean formulae, formula size, depth, symmetric Boolean functions, multiplication.