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Diskr. Mat., 1993, Volume 5, Issue 2, Pages 98–110 (Mi dm681)  

This article is cited in 3 scientific papers (total in 3 papers)

On the $id$-decompositions of the class $P_k$ over precomplete classes

S. S. Marchenkov


Abstract: We consider a representation of functions $f(x_1,\cdots,x_n)$ in $P_k$ in the form
$$ g(x_1,…,x_m,F^1_2,…,F^1_m,…,F^m_1,…,F^m_{m-1}), $$
where $2\le m\le n$ and $F^i_j=f(x_1,…,x_{j-1},x_i,x_{j+1},…,x_n)$ for $i\ne j$. We investigate the possibility of such representations with $g$ belonging to classes that are precomplete in $P_k$. We give upper bounds on the parameter $m$ in the representation.

Full text: PDF file (1481 kB)

English version:
Discrete Mathematics and Applications, 1993, 3:6, 587–599

Bibliographic databases:
UDC: 519.716
Received: 13.12.1991

Citation: S. S. Marchenkov, “On the $id$-decompositions of the class $P_k$ over precomplete classes”, Diskr. Mat., 5:2 (1993), 98–110; Discrete Math. Appl., 3:6 (1993), 587–599

Citation in format AMSBIB
\Bibitem{Mar93}
\by S.~S.~Marchenkov
\paper On the $id$-decompositions of the class~$P_k$ over precomplete classes
\jour Diskr. Mat.
\yr 1993
\vol 5
\issue 2
\pages 98--110
\mathnet{http://mi.mathnet.ru/dm681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1250960}
\zmath{https://zbmath.org/?q=an:0802.03019}
\transl
\jour Discrete Math. Appl.
\yr 1993
\vol 3
\issue 6
\pages 587--599


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. G. Parvatov, “Klony s mazhoritarnoi funktsiei i ikh obobscheniya”, Diskretn. analiz i issled. oper., 17:3 (2010), 46–60  mathnet  mathscinet  zmath
    2. S. S. Marchenkov, “The uniform $id$-decomposition of functions of many-valued logic over homogeneous functions”, Discrete Math. Appl., 20:5-6 (2010), 611–620  mathnet  crossref  crossref  mathscinet  elib
    3. P. B. Tarasov, “Certain sufficient conditions of uniformity for systems of functions of many-valued logic”, Moscow University Mathematics Bulletin, 68:5 (2013), 253–257  mathnet  crossref  mathscinet
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