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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Bibliographic Details
Published in:Automatic control and computer sciences Vol. 51; no. 5; pp. 285 - 293
Main Author: Suprun, V. P.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.09.2017
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0146-4116
1558-108X
DOI:10.3103/S0146411617050078