This article is cited in 12 papers

Mathematics

The criteria of completeness for redefining boolean function

V. I. Panteleev

Institute of Mathematics, Economics and Informatics of Irkutsk State University, Irkutsk, 664003, Russia

Abstract: Boolean functions, determined not to all sets are considered in this work. At the same time vagueness is appreciated as decision-making in the model with three possible answers: “for”, “against” and “indifferently or not determined” and decision “for” is taken in the situation “absence of against”. Appropriate definition of superposition, closed classes is introduced and the criteria of completeness is proved.

Keywords: boolean functions, partial boolean functions, closed classes, maximal classes, clone, hyperclone.

UDC: 519.716

Received: 12.02.2009
Revised: 12.02.2009