Geodesic
Construction of noniterated Boolean functions in the basis $\{\,\vee,-\}$ and estimation of their number
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 17-24

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider noniterated Boolean functions in the basis $\{\,\vee,-\}$. We obtain the canonical form of the formula for a noniterated function in this basis. We construct the set of such formulas in terms of the variables $x_1,\dots,x_n$ and calculate the number of its elements. Based on these results, we obtain the upper and lower bounds for the number of noniterated Boolean functions of $n$ variables in the basis under consideration.
Keywords: noniterated Boolean function, number of noniterated functions, estimates for the number of noniterated functions. 
@article{IVM_2008_10_a1,
     author = {O. V. Zubkov},
     title = {Construction of noniterated {Boolean} functions in the basis $\{\&,\vee,-\}$ and estimation of their number},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {17--24},
     publisher = {mathdoc},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_10_a1/}
}
TY  - JOUR
AU  - O. V. Zubkov
TI  - Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 17
EP  - 24
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_10_a1/
LA  - ru
ID  - IVM_2008_10_a1
ER  - 
%0 Journal Article
%A O. V. Zubkov
%T Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 17-24
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_10_a1/
%G ru
%F IVM_2008_10_a1
O. V. Zubkov. Construction of noniterated Boolean functions in the basis $\{\&,\vee,-\}$ and estimation of their number. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 17-24. http://geodesic.mathdoc.fr/item/IVM_2008_10_a1/