RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 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)
First page: PDF file
References: PDF file   HTML file

UDC: 519.716.325+519.1:519.21
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}