Geodesic
On the problem of implementation of Boolean functions by generalized $\alpha$-formulas
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 116-122

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper, we consider the problem of implementation of Boolean functions by generalized $\alpha$-formulas. The notion of a generalized $\alpha$-formula is introduced. For a given set of Boolean functions, we define the notion of a universal set of generalized $\alpha$-formulas. We also propose the notion of dual generalized $\alpha$-formulas and formulate the principle of duality for generalized $\alpha$-formulas. The presence of universal sets of generalized $\alpha$-formulas is proved for every $n\geq2$ for the sets $T_0(n)$ and $T_1(n)$ of $0$-preserving and $1$-preserving Boolean functions of the variables $x_1,x_2,\dots,x_n$.
Keywords: Boolean function, implementation of functions by formulas.
Mots-clés : formula 
@article{UZKU_2014_156_3_a11,
     author = {L. N. Sysoeva},
     title = {On the problem of implementation of {Boolean} functions by generalized $\alpha$-formulas},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {116--122},
     publisher = {mathdoc},
     volume = {156},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a11/}
}
TY  - JOUR
AU  - L. N. Sysoeva
TI  - On the problem of implementation of Boolean functions by generalized $\alpha$-formulas
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2014
SP  - 116
EP  - 122
VL  - 156
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a11/
LA  - ru
ID  - UZKU_2014_156_3_a11
ER  - 
%0 Journal Article
%A L. N. Sysoeva
%T On the problem of implementation of Boolean functions by generalized $\alpha$-formulas
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2014
%P 116-122
%V 156
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a11/
%G ru
%F UZKU_2014_156_3_a11
L. N. Sysoeva. On the problem of implementation of Boolean functions by generalized $\alpha$-formulas. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 116-122. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a11/