Estimates of the degrees of separating polynomials for monotone and
self-dual functions

Nosov Michail Vasilevich

Estimates of the degrees of separating polynomials for monotone and self-dual functions

Nosov M. V.

Nosov Michail Vasilevich

senior researcher, Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Chair of Mathematical Theory of Intellectual Systems

Published: 2023, vol. 27, issue 2, pp. 79–82

Download full text (In Russian)

Abstract

In this paper, we obtain an upper bound on the degree of a polynomial with real coefficients separating zeros and ones of a monotone Boolean function in the odd case of the dimension of space. Together with the previously known estimates for the even case and the lower estimate for the odd one, the ﬁnal result is obtained. Similar results are obtained for the class of self-dual functions.

Keywords: monotone Boolean function, self-dual Boolean function, separating polynomial.

BibTeX

@article{IS-Nosov2023,
  author  = {Nosov, Michail Vasilevich},
  title   = {{Estimates of the degrees of separating polynomials for monotone and self-dual functions}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2023},
  volume  = {27},
  number  = {2},
  pages   = {79--82},
}

AMSBIB

\Bibitem{IS-Nosov2023}
\by M.\,V.~Nosov
\paper Estimates of the degrees of separating polynomials for monotone and self-dual functions
\jour Intelligent Systems. Theory and Applications
\yr 2023
\vol 27
\issue 2
\pages 79--82
\lang In Russian

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