This article is cited in 5 papers

On closed classes of a $k$-valued logics functions defined by a single endomorphism

S. S. Marchenkov

Lomonosov Moscow State University, Moscow, Russia

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.

UDC: 519.716

Received: 08.04.2009

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