This article is cited in 4 papers

$A$-closed classes of many-valued logic that contain constants

S. S. Marchenkov


Abstract: The $A$-closure in the set $P_k$ of functions of $k$-valued logic is defined as the closure with respect to the operations of superposition and passing to the dual functions for even permutations of the set $E_k=\{0,1,\ldots, k-1\}$. For any $k$, $k\ge4$, all $A$-closed classes of $P_k$ containing constants are described. As a corollary, we obtain the description of all $A$-closed classes contained in the Slupecki class as well as an $A$-classification of the symmetric semigroup of mappings of the set $E_k$ into itself.
This research was supported by the Russian Foundation for Basic Research, grant 97–01–00089.

UDC: 519.7

Received: 28.08.1997
Revised: 28.01.1998

DOI: 10.4213/dm436

 English version: Discrete Mathematics and Applications, 1998, 8:4, 357–374

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