The complexity of subcube partition relates to the additive structure of the support

The subcube partition of a Boolean function is a partition of {0,1}n into the union of subcubes ∪iCi, such that the value of the function f is the same on each vector of Ci, i.e. for every i and x,y∈Ci, f(x)=f(y). The complexity of it denotes by HSCP(f) is the minimum number of subcubes in a subcube...

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Bibliographic Details
Published in:Information and computation Vol. 299; p. 105170
Main Author: Hegyvári, Norbert
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2024
Subjects:
Additive combinatorics
Bernstein theorem
Boolean cube
Fourier analysis
Harper
Fourier analysis
Boolean cube
Additive combinatorics
Bernstein theorem
Harper
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:The subcube partition of a Boolean function is a partition of {0,1}n into the union of subcubes ∪iCi, such that the value of the function f is the same on each vector of Ci, i.e. for every i and x,y∈Ci, f(x)=f(y). The complexity of it denotes by HSCP(f) is the minimum number of subcubes in a subcube partition which computes the Boolean function f. We give a lower bound of the complexity of subcube partitions of Boolean function which relates the additive behaviour of the support and the influence of the function.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2024.105170