Upper estimate of realization complexity of linear functions in a basis consisting of multi-input elements

The paper is focused on realization of parity functions by circuits in the basis U ∞ . This basis contains all functions of the form . A method of construction of circuits for a parity function of n variables with the complexity is described. This improves the previously known upper bound of U ∞ -co...

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Bibliographic Details
Published in:Moscow University mathematics bulletin Vol. 70; no. 5; pp. 226 - 229
Main Author: Kombarov, Yu. A.
Format: Journal Article
Language:English
Published: New York Allerton Press 01.09.2015
Subjects:
Analysis
Brief Communications
Mathematics
Mathematics and Statistics
Parity Function
Linear Function
Realization Complexity
ISSN:0027-1322, 1934-8444
Online Access:Get full text
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Summary:The paper is focused on realization of parity functions by circuits in the basis U ∞ . This basis contains all functions of the form . A method of construction of circuits for a parity function of n variables with the complexity is described. This improves the previously known upper bound of U ∞ -complexity of parity functions that was . The minimality of constructed circuits is verified for very small n (for n < 7).
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132215050083