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JOURNALS // Diskretnaya Matematika // Archive

Diskr. Mat., 2005 Volume 17, Issue 2, Pages 127–138 (Mi dm104)

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


 English version:
Discrete Mathematics and Applications, 2005, 15:3, 299–311

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© Steklov Math. Inst. of RAS, 2025