Geodesic
Repetition-free functions of the algebra of logic in pre-elementary
Algebra i logika, Tome 58 (2019) no. 2, pp. 271-284

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Functions of the algebra of logic that can be realized by repetition-free formulas over finite bases are studied. Necessary and sufficient conditions are derived under which functions of the algebra of logic are repetition-free in pre-elementary bases $\{-,\cdot,\vee,0,1,x_1\cdot\ldots\cdot x_n\vee \bar{x}_1\cdot\ldots\cdot \bar{x}_n\}$ and $\{-,\cdot,\vee,0,1,x_1(x_2\vee x_3\cdot\ldots\cdot x_n)\vee x_2\bar{x}_3 \cdot\ldots\cdot\bar{x}_n\}$ where $n\geq 4$. This completes the description of classes of repetition-free functions of the algebra of logic in all pre-elementary bases.
Keywords: functions of algebra of logic, repetition-free function, pre-elementary basis
Mots-clés : formula. 
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     author = {I. K. Sharankhaev},
     title = {Repetition-free functions of the algebra of logic in pre-elementary},
     journal = {Algebra i logika},
     pages = {271--284},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_2_a7/}
}
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I. K. Sharankhaev. Repetition-free functions of the algebra of logic in pre-elementary. Algebra i logika, Tome 58 (2019) no. 2, pp. 271-284. http://geodesic.mathdoc.fr/item/AL_2019_58_2_a7/