Geodesic
Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55

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In the paper, we prove the $\alpha$-completeness of finite systems of function of $k$-valued logic for $k=3,4$ containing all permutations of the symmetric group $S_k$ on the set $E_k=\{0,1,\dots,k-1\}$, the operation of addition modulo $k$, and $k$ certain binary operation. This result is extended to some other systems of functions which are obtained by replacing the operation of addition by some quasi-group operation. 
@article{DM_2006_18_4_a4,
     author = {A. L. Shabunin},
     title = {Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$},
     journal = {Diskretnaya Matematika},
     pages = {45--55},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/}
}
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A. L. Shabunin. Examples of $\alpha$-complete systems of $k$-valued logic for $k=3,4$. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 45-55. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a4/