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Fundam. Prikl. Mat., 2015, Volume 20, Issue 6, Pages 155–158 (Mi fpm1691)  

On the depth of $k$-valued logic functions over arbitrary bases

A. V. Kochergin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: The behavior of the Shannon function of the depth of $k$-valued logic functions realized by circuits over an arbitrary complete basis is examined. For all $k$, $k \ge 3$, for an arbitrary basis of $k$-valued logic functions, the existence of the asymptotic behavior of the Shannon function of the depth is established. The asymptotic behavior is linear for finite bases and it is constant or logarithmic for infinite bases. Thus, the complete picture of asymptotic behavior of the Shannon function of the depth is obtained for all $k$, $k \ge 2$.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00598_a
Russian Academy of Sciences - Federal Agency for Scientific Organizations


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English version:
Journal of Mathematical Sciences (New York), 2018, 233:1, 100–102

UDC: 519.7

Citation: A. V. Kochergin, “On the depth of $k$-valued logic functions over arbitrary bases”, Fundam. Prikl. Mat., 20:6 (2015), 155–158; J. Math. Sci., 233:1 (2018), 100–102

Citation in format AMSBIB
\Bibitem{Koc15}
\by A.~V.~Kochergin
\paper On the depth of $k$-valued logic functions over arbitrary bases
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 6
\pages 155--158
\mathnet{http://mi.mathnet.ru/fpm1691}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 233
\issue 1
\pages 100--102
\crossref{https://doi.org/10.1007/s10958-018-3927-5}


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