Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 102-104
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S. F. Vinokurov; N. A. Peryazev. Decomposition of Boolean functions into the sum of products of subfunctions. Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 102-104. http://geodesic.mathdoc.fr/item/DM_1993_5_3_a8/
@article{DM_1993_5_3_a8,
author = {S. F. Vinokurov and N. A. Peryazev},
title = {Decomposition of {Boolean} functions into the sum of products of subfunctions},
journal = {Diskretnaya Matematika},
pages = {102--104},
year = {1993},
volume = {5},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1993_5_3_a8/}
}
TY - JOUR
AU - S. F. Vinokurov
AU - N. A. Peryazev
TI - Decomposition of Boolean functions into the sum of products of subfunctions
JO - Diskretnaya Matematika
PY - 1993
SP - 102
EP - 104
VL - 5
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_1993_5_3_a8/
LA - ru
ID - DM_1993_5_3_a8
ER -
%0 Journal Article
%A S. F. Vinokurov
%A N. A. Peryazev
%T Decomposition of Boolean functions into the sum of products of subfunctions
%J Diskretnaya Matematika
%D 1993
%P 102-104
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1993_5_3_a8/
%G ru
%F DM_1993_5_3_a8
We obtain a theorem on the representation of Boolean functions in the polynomial form $$ f(x,y)=\sum_\sigma\sum_\tau\alpha_{\tau\sigma}f(\tau,y)f(x,\sigma), $$ where the Boolean summations are taken over all Boolean vectors $\sigma$ and $\tau$, $\alpha_{\tau\sigma}\in\{0,1\}$, $x$ and $y$ are collections of Boolean variables. We also give a method for finding the coefficients $\alpha_{\tau\sigma}$.
