Geodesic
Closed classes of three-valued logic functions generated by symmetric functions with a~bounded number of layers
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 17-26

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Closed classes of three-valued logic functions of which a generating system consists of symmetric functions with values in the set $\{0,1\}$ and with value 1 at a bounded subset of layers from $\{1,2\}^n$ are considered. Some criteria for existence of a basis and of a finite basis are obtained for these classes. It is shown how the existence of a basis or of a finite basis depends on the existence of a basis or of a finite basis in subclasses generated by monotonous or non-monotonous functions.
Keywords: multi-valued logic functions, closed classes, generating systems. 
@article{PDM_2015_1_a1,
     author = {A. V. Mikhailovich},
     title = {Closed classes of three-valued logic functions generated by symmetric functions with a~bounded number of layers},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {17--26},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_1_a1/}
}
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A. V. Mikhailovich. Closed classes of three-valued logic functions generated by symmetric functions with a~bounded number of layers. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 17-26. http://geodesic.mathdoc.fr/item/PDM_2015_1_a1/