NDLI: Order of the length of Boolean functions in the class of exclusive-OR sums of pseudoproducts

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Order of the length of Boolean functions in the class of exclusive-OR sums of pseudoproducts

Content Provider	Springer Nature Link
Author	Selezneva, S. N.
Copyright Year	2016
Abstract	An exclusive-OR sum of pseudoproducts (ESPP) is a modufo-2 sum of products of affine (linear) Boolean functions. The length of an ESPP is defined as the number of summands in this sum; the length of a Boolean function in the class of ESPPs is the minimum length of an ESPP representing this function. The Shannon length function L $^{ESPP}$(n) on the set of Boolean functions in the class of ESPPs is considered; it is defined as the maximum length of a Boolean function of n variables in the class of ESPPs. It is proved that L $^{ESPP}$(n) = Ɵ (2$^{ n }$/n $^{2}$). The quantity L $^{ESPP}$(n) also equals the least number l such that any Boolean function of n variables can be represented as a modulo-2 sum of at most l multiaffine functions.
Starting Page	123
Ending Page	127
Page Count	5
File Format	PDF
ISSN	02786419
Journal	Moscow University Computational Mathematics and Cybernetics
Volume Number	40
Issue Number	3
e-ISSN	19348428
Language	English
Publisher	Allerton Press
Publisher Date	2016-09-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Boolean function polynomial form Zhegalkin polynomial exclusive-OR sum of pseudoproducts length upper bound multiaffine function Mathematics
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Human-Computer Interaction Computational Mathematics

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