Geodesic
On the closed classes of $k$-valued logic functions taking no more than three values
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 98-109

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The paper considers $k$-valued logic functions where $k=2^m$, $m\geq2$. A $\beta$-closure operator is defined based on their encoding in the binary numeral system. A special mapping of all $\beta$-closed classes to a set of closed classes of Boolean functions is denoted. The cardinality of a set of $\beta$-closed classes which are mapped to a class $\mathcal B$ and contain only functions taking no more than three values is studied in this paper for each class $\mathcal B$ of Boolean functions.
Keywords: multi-valued logic, closed classes, closure operator, $\beta$-closure, superposition strengthening, binary superposition. 
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     author = {D. K. Podolko},
     title = {On the closed classes of $k$-valued logic functions taking no more than three values},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {98--109},
     publisher = {mathdoc},
     volume = {156},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a9/}
}
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D. K. Podolko. On the closed classes of $k$-valued logic functions taking no more than three values. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 98-109. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a9/