Computer Science and Information Technology Vol. 5(4), pp. 140 - 147
DOI: 10.13189/csit.2017.050404
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Algebraic Objects of MBFs and Recursive Computation of the Dedekind Number

Tkachenco V.G. ^1,*, Sinyavsky O.V. ^2
1 Institute of Radio, Television, Electronics, Odessa National Academy of Telecommunications, Ukraine
² Department of Fundamental Sciences, Odessa Military Academy, Ukraine

ABSTRACT

In this article the whole set of n-1 rank Monotone Boolean Functions (MBFs) is divided into equivalence classes. It shows how the Dedekind number D(n) can be calculated by using this partition. Five formulas were found to calculate this number as well as the algebraic properties of MBF blocks.

KEYWORDS
Monotone Boolean Functions, Free Distributive Lattice, Dedekind Number, Algebraic Structures

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Tkachenco V.G. , Sinyavsky O.V. , "Algebraic Objects of MBFs and Recursive Computation of the Dedekind Number," Computer Science and Information Technology, Vol. 5, No. 4, pp. 140 - 147, 2017. DOI: 10.13189/csit.2017.050404.

(b). APA Format:
Tkachenco V.G. , Sinyavsky O.V. (2017). Algebraic Objects of MBFs and Recursive Computation of the Dedekind Number. Computer Science and Information Technology, 5(4), 140 - 147. DOI: 10.13189/csit.2017.050404.