License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2015.264
URN: urn:nbn:de:0030-drops-50663
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5066/
Servedio, Rocco A. ;
Tan, Li-Yang ;
Wright, John
Adaptivity Helps for Testing Juntas
Abstract
We give a new lower bound on the query complexity of any non-adaptive algorithm for testing whether an unknown Boolean function is a k-junta versus epsilon-far from every k-junta. Our lower bound is that any non-adaptive algorithm must make Omega(( k * log*(k)) / ( epsilon^c * log(log(k)/epsilon^c))) queries for this testing problem, where c is any absolute constant <1. For suitable values of epsilon this is asymptotically larger than the O(k * log(k) + k/epsilon) query complexity of the best known adaptive algorithm [Blais,STOC'09] for testing juntas, and thus the new lower bound shows that adaptive algorithms are more powerful than non-adaptive algorithms for the junta testing problem.
BibTeX - Entry
@InProceedings{servedio_et_al:LIPIcs:2015:5066,
author = {Rocco A. Servedio and Li-Yang Tan and John Wright},
title = {{Adaptivity Helps for Testing Juntas}},
booktitle = {30th Conference on Computational Complexity (CCC 2015)},
pages = {264--279},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-81-1},
ISSN = {1868-8969},
year = {2015},
volume = {33},
editor = {David Zuckerman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5066},
URN = {urn:nbn:de:0030-drops-50663},
doi = {10.4230/LIPIcs.CCC.2015.264},
annote = {Keywords: Property testing, juntas, adaptivity}
}
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Keywords: |
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Property testing, juntas, adaptivity |
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Collection: |
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30th Conference on Computational Complexity (CCC 2015) |
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Issue Date: |
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2015 |
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Date of publication: |
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06.06.2015 |
