We consider the problem of approximation of a random Boolean function by elements of the set of all Boolean functions of degree no greater than two, i.e., by the quadratic forms. It is proved that the Hamming distance from a random Boolean function of η variables to the set of all quadratic forms has in limit as η -» oo the double exponential distribution.
The spectral complexity of a Boolean function is the number of non-zero coefficients of the Fourier-Walsh expansion of the function. Asymptotic estimates of the moments of the spectral complexity of a random Boolean function of n variables as n -> oo are obtained. These estimates show that the part of non-complicated (in a sense) functions tends to zero as n -> oo.
We consider the distribution of the sum of independent random variables which take their values from a primary cyclic group and are uniformly distributed on sets of identical cardinality.
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