Aleksandr Aleksandrovich Serov

Aleksandr Aleksandrovich Serov
Russian Academy of Sciences | RAS · Steklov Mathematical Institute

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20
Publications
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98
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Introduction
Aleksandr Aleksandrovich Serov currently works at the Steklov Mathematical Institute, Russian Academy of Sciences. Aleksandr does research in Statistics, Probability Theory and Applied Mathematics. Their most recent publication is 'Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set'.

Publications

Publications (20)
Article
Рассматриваются явные рекуррентные формулы для чисел последовательностей, содержащих заданный шаблон заданное число раз, зависящие только от длины последовательности, длины шаблона и его периода. Эти формулы позволяют находить характеристики теста перекрывающихся шаблонов из пакета NIST для двоичных последовательностей и произвольных параметров шаб...
Article
Let X N be a set of N elements and F1 , F2 ,… be a sequence of random independent equiprobable mappings X N → N . For a subset S0 ⊂ X N , | S0 |= m , we consider a sequence of its images St = Ft (… F2 ( F1 ( S0 ))…), t =1,2… An approach to the exact recurrent computation of distribution of | St | is described. Two-sided inequalities for M {| St |||...
Article
Let 𝓧 𝓝 be a set consisting of N elements and F1 , F2 , … be a sequence of random independent equiprobable mappings 𝓧 𝓝 → 𝓧 𝓝 . For a subset S0 ⊂ 𝓧 𝓝 , | S0 | = n , we consider a sequence of its images S t = F t (… F2 ( F1 ( S0 ))…), t = 1, 2 … The conditions on n , t , N → ∞ under which the distributions of image sizes | S t | are asymptotically c...
Article
For random equiprobable Boolean functions we investigate the distribution of the number of subfunctions which have a given number of variables and are close to the set of affine Boolean functions. It is shown, for example, that for Boolean functions of n variables the mean number of subfunctions having s ⩾ 3 + log2n variables and the Hamming distan...
Article
Let N be a set of N elements and F1,G1,F2,G2,… be a sequence of independent pairs of random dependent mappings N→N such that Fk and Gk are random equiprobable mappings and P{Fk(x)=Gk(x)}=α for all x∈N and k = 1, 2, … For a subset S0⊂N,|S0|=n, we consider a sequences of its images Sk=Fk(…F2(F1(S0))…), Tk=Gk(…G2(G1(S0))…), k = 1, 2 …, and a sequences...
Article
Let N be a set of N elements and F1, F2,... be a sequence of random independent equiprobable mappings N → N. For a subset S0 C N, S0= n, we consider a sequence of its images Sk = Fk(...F2(F1(S0))...), k=1,2..., and a sequence of their unions Ψk = S1 U...U Sk, k = 1, 2... An approach to the exact computation of distribution of Sk and Ψk for moderate...
Article
We obtain two-sided bounds and asymptotic formulas for the number of Boolean functions of n variables which are approximated by quadratic Boolean functions to a given accuracy. This research was supported by the Russian Foundation for Basic Research, grant 11-01- 00139.
Article
Full-text available
We present a new form and a short complete proof of explicit two-sided estimates for the distribution function F n,p (k) of the binomial law with parameters n,p from D. Alfers and H. H. Dinges [Z. Wahrscheinlichkeitstheor. Verw. Geb. 65, 399–420 (1984; Zbl 0506.62011)]. These inequalities are universal (valid for all values of parameters and argume...
Article
A limit theorem for the Hamming distance of a random Boolean function of n Boolean variables with uniform distribution to the set of affine functions is proved. The results are compared with a similar theorem proved by Ryazanov for the distance to the set of linear functions.
Article
We obtain two-sided bounds and asymptotic formulas for the number of Boolean functions of n variables which are approximated by affine or linear Boolean functions with a given accuracy.

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