An analogue of the Slupecki maximal clone within the clone of
polynomials modulo four

Yanushkevich Ivan Mikhailovich

An analogue of the Slupecki maximal clone within the clone of polynomials modulo four

Yanushkevich I. M.

Yanushkevich Ivan Mikhailovich

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

0009-0005-6128-9519

Received: 30 Mar 2026 Accepted: 02 Apr 2026

Published: 2026, vol. 30, issue 2, pp. 142–156

Download full text (In Russian)

Abstract

We study the clone of all functions on four elements that can be represented as polynomials modulo 4. We show that any such function is uniquely determined by a set of Boolean functions of the same arity. The main result of the paper is a description of a maximal clone within the clone of polynomial functions that contains all unary polynomials, and which is analogous to the Słupecky maximal clone.

Keywords: multivalued logic function, polynomial, closed class.

BibTeX

@article{IS-Yanushkevich2026,
  author  = {Yanushkevich, Ivan Mikhailovich},
  title   = {{An analogue of the Slupecki maximal clone within the clone of polynomials modulo four}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2026},
  volume  = {30},
  number  = {2},
  pages   = {142--156},
}

AMSBIB

\Bibitem{IS-Yanushkevich2026}
\by I.\,M.~Yanushkevich
\paper An analogue of the Slupecki maximal clone within the clone of polynomials modulo four
\jour Intelligent Systems. Theory and Applications
\yr 2026
\vol 30
\issue 2
\pages 142--156
\lang In Russian

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