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Mat. Zametki, 2009, Volume 86, Issue 4, Pages 550–556 (Mi mz4433)  

This article is cited in 3 scientific papers (total in 3 papers)

Orders of Discriminator Classes in Multivalued Logic

S. S. Marchenkov

M. V. Lomonosov Moscow State University

Abstract: For $k\ge2$, discriminator classes, that is, closed classes of functions of $k$-valued logic containing the ternary discriminator $p$, are considered. It is proved that any discriminator class has order at most $\max(3,k)$; moreover, the order of any discriminator class containing all homogeneous functions does not exceed $\max(3,k-1)$, and the order of a discriminator class containing all even functions does not exceed $\max(3,k-2)$. All of these three bounds are attainable.

Keywords: function of multivalued logic, discriminator class of functions, ternary discriminator, structure homogeneous functions, homogeneous functions, even functions

DOI: https://doi.org/10.4213/mzm4433

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English version:
Mathematical Notes, 2009, 86:4, 516–521

Bibliographic databases:

UDC: 519.716
Received: 09.01.2008

Citation: S. S. Marchenkov, “Orders of Discriminator Classes in Multivalued Logic”, Mat. Zametki, 86:4 (2009), 550–556; Math. Notes, 86:4 (2009), 516–521

Citation in format AMSBIB
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\paper Orders of Discriminator Classes in Multivalued Logic
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\vol 86
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\pages 550--556
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\pages 516--521
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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. S. S. Marchenkov, “The closure operator in many-valued logic based on functional equations”, J. Appl. Industr. Math., 5:3 (2011), 383–390  mathnet  crossref  mathscinet  zmath
    2. Marchenkov S.S., “On orders of closed classes containing a homogeneous switching function”, Mosc. Univ. Comput. Math. Cybern., 36:3 (2012), 145–149  crossref  mathscinet  zmath  elib  elib  scopus
    3. S. S. Marchenkov, “Closed classed of three-valued logic that contain essentially multiplace functions”, Discrete Math. Appl., 25:4 (2015), 233–240  mathnet  crossref  crossref  mathscinet  isi  elib
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