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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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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/

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