Diskr. Mat., 2005 Volume 17, Issue 2, Pages 127–138
(Mi dm104)
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This article is cited in
6 papers
Criteria for Boolean functions to be repetition-free in pre-elementary bases of rank 3
N. A. Peryazev,
I. K. Sharankhaev
Abstract:
We study representations of Boolean functions by formulas and
describe in terms of remainder functions the classes of repetition-free Boolean
functions in the pre-elementary bases
\begin{gather*}
\{\vee, \cdot, -, 0, 1, x_1x_2x_3 \vee \bar{x}_1\bar{x}_2\bar{x}_3\},
\qquad
\{\vee, \cdot, -, 0, 1, x_1(x_2 \vee x_3) \vee x_2x_3\},\\
\{\vee, \cdot, -, 0, 1, x_1(x_2 \vee x_3) \vee x_2\bar{x}_3\}.
\end{gather*}
UDC:
519.71 Received: 24.05.2004
DOI:
10.4213/dm104
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