Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"
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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2022, Volume 14, Issue 4, Pages 20–27
DOI: https://doi.org/10.14529/mmph220403 (Mi vyurm533) 		 
Mathematics

Minimization of representations of the logical function in Schaeffer and Pierce bases

V. V. Menshikh, V. A. Nikitenko

Voronezh Institute of the Ministry of Internal Affairs of Russia, Voronezh, Russian Federation
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DOI: https://doi.org/10.14529/mmph220403
Abstract: The paper studies the representation of arbitrary logical functions in Schaeffer and Pierce bases. For this purpose, recurrent dependencies of the representation of disjunctive and conjunctive monomials in these bases were initially established. Then generalizations were made to the arbitrary logical formulas presented in the form of disjunctive and conjunctive normal forms. Estimates were obtained for the number of operations in logical formulas during the transition to the Schaeffer and Pierce bases.
Keywords: disjunctive monomial, conjunctive monomial, Schaeffer's basis, Pierce's basis, Boolean variable, Boolean function.
Received: 18.07.2022
Document Type: Article
UDC: 510.63
Language: Russian
Citation: V. V. Menshikh, V. A. Nikitenko, “Minimization of representations of the logical function in Schaeffer and Pierce bases”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 14:4 (2022), 20–27
Citation in format AMSBIB
\Bibitem{MenNik22}
\by V.~V.~Menshikh, V.~A.~Nikitenko
\paper Minimization of representations of the logical function in Schaeffer and Pierce bases
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2022
\vol 14
\issue 4
\pages 20--27
\mathnet{http://mi.mathnet.ru/vyurm533}
\crossref{https://doi.org/10.14529/mmph220403}
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