Complexity of linear and majority functions in the basis of antichain functions

The complexity of realization of Boolean functions by circuits of functional elements in the basis consisting of all characteristic functions of antichains over a Boolean cube is studied. It is proved that the complexity of realization of an n -variable parity function is and the complexity of its n...

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Vydáno v:Moscow University mathematics bulletin Ročník 71; číslo 2; s. 82 - 83
Hlavní autor: Podolskaya, O. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Allerton Press 01.03.2016
Témata:
Analysis
Brief Communications
Mathematics
Mathematics and Statistics
Characteristic Function
Boolean Function
Parity Function
Majority Function
Functional Element
ISSN:0027-1322, 1934-8444
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Shrnutí:The complexity of realization of Boolean functions by circuits of functional elements in the basis consisting of all characteristic functions of antichains over a Boolean cube is studied. It is proved that the complexity of realization of an n -variable parity function is and the complexity of its negation equals the complexity of the n -variable majority function which is .
ISSN:0027-1322
1934-8444
DOI:10.3103/S002713221602008X