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Diskr. Mat., 2020, Volume 32, Issue 2, Pages 61–70 (Mi dm1602)  

On the degree of restrictions of $q$-valued logic vector functions to linear manifolds

V. G. Ryabov

NP «GST»

Abstract: For a randomly selected of $q$-valued logic vector function and linear manifolds of a fixed dimension, the probability of occurrence of restrictions with a degree not higher than the given one is estimated, and the asymptotics of the number of manifolds on which the restrictions are affine is obtained. It is shown that if $n \to \infty$ for almost all $q$-valued logic functions of $n$ variables with $k$ coordinate functions, the value of the maximum dimension of a manifold on which the restriction is affine belongs to the segment $[\lfloor \log_q \frac{n}{k}+\log_q \log_q \frac{n}{k} \rfloor, \lceil \log_q \frac{n}{k}+\log_q \log_q \frac{n}{k} \rceil]$, while the analogous parameter for the case of fixing variables is in the range $[\lfloor \log_q \frac{n}{k} \rfloor, \lceil \log_q \frac{n}{k} \rceil]$.

Keywords: $q$-valued logic, vector function, restriction, manifold, degree.

DOI: https://doi.org/10.4213/dm1602

Full text: PDF file (555 kB)
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UDC: 519.716.325+519.1:519.21
Received: 09.12.2019
Revised: 13.05.2020

Citation: V. G. Ryabov, “On the degree of restrictions of $q$-valued logic vector functions to linear manifolds”, Diskr. Mat., 32:2 (2020), 61–70

Citation in format AMSBIB
\Bibitem{Rya20}
\by V.~G.~Ryabov
\paper On the degree of restrictions of $q$-valued logic vector functions to linear manifolds
\jour Diskr. Mat.
\yr 2020
\vol 32
\issue 2
\pages 61--70
\mathnet{http://mi.mathnet.ru/dm1602}
\crossref{https://doi.org/10.4213/dm1602}


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