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Algebra i logika, 2019, Volume 58, Number 2, Pages 271–284
DOI: https://doi.org/10.33048/alglog.2019.58.208
(Mi al894)
 

Repetition-free functions of the algebra of logic in pre-elementary bases

I. K. Sharankhaev
References:
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.
Funding agency
Supported by a grant of Buryat State University.
Received: 26.11.2017
Revised: 09.07.2019
English version:
Algebra and Logic, 2019, Volume 58, Issue 2, Pages 186–195
DOI: https://doi.org/10.1007/s10469-019-09536-0
Bibliographic databases:
Document Type: Article
UDC: 519.71
Language: Russian
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
Citation in format AMSBIB
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\by I.~K.~Sharankhaev
\paper Repetition-free functions of the algebra of logic in pre-elementary
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\yr 2019
\vol 58
\issue 2
\pages 271--284
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\jour Algebra and Logic
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\vol 58
\issue 2
\pages 186--195
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  • https://www.mathnet.ru/eng/al/v58/i2/p271
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    Алгебра и логика Algebra and Logic
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    References:25
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