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Diskretn. Anal. Issled. Oper., 2009, Volume 16, Number 6, Pages 52–67 (Mi da594)  

This article is cited in 4 scientific papers (total in 4 papers)

On closed classes of a $k$-valued logics functions defined by a single endomorphism

S. S. Marchenkov

Lomonosov Moscow State University, Moscow, Russia

Abstract: The closed classes in $P_k$ defined by a single endomorphism are investigated. It is proved that every such class is positive closed. In the case of nonidentical idempotent endomorphism the corresponding class is positive precomplete in $P_k$. For $k=2,3$ all positive precomplete classes in $P_k$ are defined by the same endomorphisms. All positive submaximal classes in $P_3$ are found. Bibl. 11.

Keywords: many-valued logic function, endomorphism, positive closed classes.

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Bibliographic databases:
UDC: 519.716
Received: 08.04.2009

Citation: S. S. Marchenkov, “On closed classes of a $k$-valued logics functions defined by a single endomorphism”, Diskretn. Anal. Issled. Oper., 16:6 (2009), 52–67

Citation in format AMSBIB
\Bibitem{Mar09}
\by S.~S.~Marchenkov
\paper On closed classes of a~$k$-valued logics functions defined by a~single endomorphism
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 6
\pages 52--67
\mathnet{http://mi.mathnet.ru/da594}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2649142}
\zmath{https://zbmath.org/?q=an:1249.03018}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Marchenkov S.S., “Operator of Positive Closure”, Dokl. Math., 85:1 (2012), 102–103  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. S. S. Marchenkov, “Atoms of the lattice of positively closed classes of three-valued logic”, Discrete Math. Appl., 22:2 (2012), 123–137  mathnet  crossref  crossref  mathscinet  elib
    3. S. S. Marchenkov, “Definition of positively closed classes by endomorphism semigroups”, Discrete Math. Appl., 22:5-6 (2012), 511–520  mathnet  crossref  crossref  mathscinet  elib
    4. S. S. Marchenkov, “Positive closed classes in the three-valued logic”, J. Appl. Industr. Math., 8:2 (2014), 256–266  mathnet  crossref  mathscinet  isi
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