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Repetition-free functions of the algebra of logic in pre-elementary
bases
I. K. Sharankhaev
Abstract:
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, formula.
Received: 26.11.2017 Revised: 09.07.2019
Citation:
I. K. Sharankhaev, “Repetition-free functions of the algebra of logic in pre-elementary
bases”, Algebra Logika, 58:2 (2019), 271–284; Algebra and Logic, 58:2 (2019), 186–195
Linking options:
https://www.mathnet.ru/eng/al894 https://www.mathnet.ru/eng/al/v58/i2/p271
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