Upper Linear Bound for the Cardinality of the Domain of a Universal
Function for Pairs of linear

Sedova Anna Sergeevna

Upper Linear Bound for the Cardinality of the Domain of a Universal Function for Pairs of linear

Sedova A. S.

Sedova Anna Sergeevna

Junior Researcher, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Chair of Information Security

0009-0009-7424-0043

Received: 30 Apr 2026 Revised: 18 May 2026 Accepted: 19 May 2026

Published: 2026, vol. 30, issue 2, pp. 74–80

Download full text (In Russian)

Abstract

Previously, the problems of existence and cardinality estimation of the domain of universal functions for various classes of functions in Boolean and \(k\)-valued logics were investigated. For the universal function for pairs of linear functions, existence was proven starting from seven variables. We obtained an upper linear bound on the cardinality of the domain of the universal function for pairs of linear functions by applying generalizations of the gradient method.

Keywords: linear function, universal function, gradient algorithm, matrix covering.

BibTeX

@article{IS-Sedova2026,
  author  = {Sedova, Anna Sergeevna},
  title   = {{Upper Linear Bound for the Cardinality of the Domain of a Universal Function for Pairs of linear}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2026},
  volume  = {30},
  number  = {2},
  pages   = {74--80},
}

AMSBIB

\Bibitem{IS-Sedova2026}
\by A.\,S.~Sedova
\paper Upper Linear Bound for the Cardinality of the Domain of a Universal Function for Pairs of linear
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 2
\pages 74--80
\lang In Russian

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