Geodesic
Criteria for Boolean functions to be repetition-free in pre-elementary bases of rank~3
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 127-138.

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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*} 
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N. A. Peryazev; I. K. Sharankhaev. Criteria for Boolean functions to be repetition-free in pre-elementary bases of rank~3. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 127-138. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a9/

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