Formulas of the General Solutions of Boolean Equations
Publications de l'Institut Mathématique, _N_S_44 (1988) no. 58, p. 9
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We explicitly give various formulas of the general solutions
of Boolean equations in $n$ unknows. The method presented in the paper
is based on a Prešić's idea of the solving function from [4], but
we have it here in more general form. We build the cycle using the
sequence $i_1,i_2,\ldots,i_{\nu}$ ($\nu = 2^n$) where
$\{i_1,i_2,\ldots,i_{\nu}\} = \{0,1,2,\ldots,\nu-1\}$. We can chose
the sequence so that we obtain the formulas of the general solution in
the triangular form. Specially, when $i_1 = 2^n-1$, we have the
reproductive solutions. This paper enables one to make the program
(we wrote it in FORTRAN IV) for digital computer which gives the
formulas of the general solutions of Boolean equations, where the
number of unknowns can be large. The limitation results only from the
number of the elements of the sequence $i_1,i_2,\ldots,i_{\nu}$ i.e. of
the memory of the computer.
Classification :
03G05
@article{PIM_1988_N_S_44_58_a1,
author = {Dragi\'c Bankovi\'c},
title = {Formulas of the {General} {Solutions} of {Boolean} {Equations}},
journal = {Publications de l'Institut Math\'ematique},
pages = {9 },
publisher = {mathdoc},
volume = {_N_S_44},
number = {58},
year = {1988},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1988_N_S_44_58_a1/}
}
Dragić Banković. Formulas of the General Solutions of Boolean Equations. Publications de l'Institut Mathématique, _N_S_44 (1988) no. 58, p. 9 . http://geodesic.mathdoc.fr/item/PIM_1988_N_S_44_58_a1/