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Diskretn. Anal. Issled. Oper., Ser. 1, 2006, Volume 13, Number 3, Pages 27–39 (Mi da34)  

This article is cited in 11 scientific papers (total in 11 papers)

A criterion for positive completeness in ternary logic

S. S. Marchenkov

M. V. Lomonosov Moscow State University

Abstract: The operator of positive closure is considered on the set $P_k$ of functions of $k$-valued logic. Some positive complete systems of functions are defined. It is proved that every positive complete class of functions from $P_k$ is positive generated by the set of all functions depending on at most $k$ variables. For each $k\geqslant 3$, the three families of positive precomplete classes are defined. It is shown that, for $k=3$, the 10 classes of these families constitute a criterion system.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:4, 481–488

Bibliographic databases:

Received: 14.02.2006

Citation: S. S. Marchenkov, “A criterion for positive completeness in ternary logic”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:3 (2006), 27–39; J. Appl. Industr. Math., 1:4 (2007), 481–488

Citation in format AMSBIB
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\by S.~S.~Marchenkov
\paper A criterion for positive completeness in ternary logic
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2006
\vol 13
\issue 3
\pages 27--39
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2289370}
\zmath{https://zbmath.org/?q=an:1249.03016}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 4
\pages 481--488
\crossref{https://doi.org/10.1134/S1990478907040114}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-37249053294}


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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. J. Appl. Industr. Math., 2:4 (2008), 542–549  mathnet  crossref  mathscinet  zmath
    2. Marchenkov S.S., “Strong closure operators on the set of partial Boolean functions”, Doklady Mathematics, 77:2 (2008), 288–289  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. S. Marchenkov, “Positively closed classes of three-valued logic generated by one-place functions”, Discrete Math. Appl., 19:4 (2009), 375–382  mathnet  crossref  crossref  mathscinet  elib
    4. S. S. Marchenkov, “O zamknutykh klassakh funktsii $k$-znachnoi logiki, opredelyaemykh odnim endomorfizmom”, Diskretn. analiz i issled. oper., 16:6 (2009), 52–67  mathnet  mathscinet  zmath
    5. L. G. Afraimovich, M. Kh. Prilutskii, “Multiindex optimal production planning problems”, Autom. Remote Control, 71:10 (2010), 2145–2151  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. Marchenkov S.S., “Operator of positive closure”, Dokl. Math., 85:1 (2012), 102–103  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. 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
    8. 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
    9. S. S. Marchenkov, “Positive closed classes in the three-valued logic”, J. Appl. Industr. Math., 8:2 (2014), 256–266  mathnet  crossref  mathscinet  isi
    10. S. S. Marchenkov, A. V. Chernyshev, “Basic positively closed classes in three-valued logic”, Discrete Math. Appl., 28:3 (2018), 157–165  mathnet  crossref  crossref  isi  elib
    11. S. S. Marchenkov, “Kriterii polnoty dlya operatora zamykaniya po perechisleniyu v trekhznachnoi logike”, Diskret. matem., 30:4 (2018), 47–54  mathnet  crossref  elib
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