Volume 16, No 6, 2009, P. 52-67

UDC 519.716
S. S. Marchenkov
On closed classes of a $k$-valued logics functions defined by a single endomorphism

Abstract:
The closed classes in $P_k$ defined by a single endomorphism are investigated. It is proved that every such class is positive closed. In the case of nonidentical idempotent endomorphism the corresponding class is positive precomplete in $P_k$. For $k=2,3$ all positive precomplete classes in $P_k$ are defined by the same endomorphisms. All positive submaximal classes in $P_3$ are found.
Bibl. 11.

Keywords: many-valued logic function, endomorphism, positive closed classes.

Marchenkov Sergey Serafimovich ¹
1. Lomonosov Moscow State University,
Vorob’evy ghory, 119992 Moscow, Russia
e-mail: mathcyb@cs.msu.su