Geodesic
The uniform $id$-decomposition of functions of many-valued logic over homogeneous functions
Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 55-63 
S. S. Marchenkov. The uniform $id$-decomposition of functions of many-valued logic over homogeneous functions. Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 55-63. http://geodesic.mathdoc.fr/item/DM_2010_22_4_a4/
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     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_4_a4/}
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We consider the uniform $id$-decomposition of functions of the class $P_k$ of functions of $k$-valued logic over the class $H^*_k$ of structural homogeneous functions and the class $D_k$ of homogeneous functions generated by the dual discriminator $d$. We find the degrees of the uniform $id$-decomposition of the class $P_k$ over the classes $H^*_k$ and $D_k$ and give the methods of construction of homogeneous functions over which the uniform $id$-decomposition of the class $P_k$ is realised.

[1] Marchenkov S. S., “Odnorodnye algebry”, Problemy kibernetiki, 39, 1982, 85–106 | MR | Zbl

[2] Marchenkov S. S., “O ravnomernom $id$-razlozhenii bulevykh funktsii”, Diskretnaya matematika, 2:3 (1990), 29–41 | MR | Zbl

[3] Marchenkov S. S., “O stepeni ravnomernogo $id$-razlozheniya zamknutykh klassov v $P_k$”, Diskretnaya matematika, 3:4 (1991), 128–142 | MR | Zbl

[4] Marchenkov S. S., “Ob $id$-razlozheniyakh klassa $P_k$ nad predpolnymi klassami”, Diskretnaya matematika, 5:2 (1993), 98–110 | MR | Zbl

[5] Marchenkov S. S., Zamknutye klassy bulevykh funktsii, Fizmatlit, Moskva, 2000 | MR | Zbl

[6] Yablonskii S. V., Vvedenie v diskretnuyu matematiku, Nauka, Moskva, 1986 | MR

[7] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, Moskva, 1966 | MR

[8] Marczewski E., “Homogeneous operations and homogeneous algebras”, Fundam. Math., 56 (1964), 81–103 | MR | Zbl