Computer Science and Information Technology Vol. 4(4), pp. 139 - 146
DOI: 10.13189/csit.2016.040402
Reprint (PDF) (408Kb)


Blocks of Monotone Boolean Functions of Rank 5


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

ABSTRACT

Based on the classification of monotone Boolean functions (MBFs) on the types and the method of building MBFs blocks, an analysis is conducted of the MBFs rank 5. Four matrixes for such MBFs are adduced. It is shown that there are 7581 MBFs rank 5, 276 of them are MBFs of maximal types. These 7581 MBFs are contained in 522 blocks or 23 groups of isomorphic blocks or 6 groups of similar blocks. The offered methods can be used to analyze large MBFs ranks. In previous articles were shown how MBFs used in telecommunications for analyzing networks and building codes for cryptosystems.

KEYWORDS
Monotone Boolean Functions, Disjunctive Complement, Conjunctive Complement, Dedekind Number, Free Distributive Lattice

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Tkachenco V.G. , Sinyavsky O.V. , "Blocks of Monotone Boolean Functions of Rank 5," Computer Science and Information Technology, Vol. 4, No. 4, pp. 139 - 146, 2016. DOI: 10.13189/csit.2016.040402.

(b). APA Format:
Tkachenco V.G. , Sinyavsky O.V. (2016). Blocks of Monotone Boolean Functions of Rank 5. Computer Science and Information Technology, 4(4), 139 - 146. DOI: 10.13189/csit.2016.040402.