The complexity of Boolean functions in the Reed–Muller polynomials class

This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functio...

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Vydáno v:Automatic control and computer sciences Ročník 51; číslo 5; s. 285 - 293
Hlavní autor: Suprun, V. P.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.09.2017
Springer Nature B.V
Témata:
Boolean algebra
Boolean functions
Codes
Complexity
Computer Science
Control Structures and Microprogramming
Functions (mathematics)
Mathematical analysis
Polynomials
polynomial complexity
Reed–Muller polynomial
Zhegalkin polynomial
symmetric Boolean function
triangle method
logical scheme
Boolean function
Shannon functions
Boolean derivative
ISSN:0146-4116, 1558-108X
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Shrnutí:This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0146-4116
1558-108X
DOI:10.3103/S0146411617050078