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.2017.26
URN: urn:nbn:de:0030-drops-75283
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7528/
Chen, Xi ;
Servedio, Rocco A. ;
Tan, Li-Yang ;
Waingarten, Erik ;
Xie, Jinyu
Settling the Query Complexity of Non-Adaptive Junta Testing
Abstract
We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f is a k-junta or epsilon-far from every k-junta must make ~Omega(k^{3/2}/ epsilon) many queries for a wide range of parameters k and epsilon. Our result dramatically improves previous lower bounds from [BGSMdW13,STW15], and is essentially optimal given Blais's non-adaptive junta tester from [Blais08], which makes ~O(k^{3/2})/epsilon queries. Combined with the adaptive tester of [Blais09] which makes O(k log k + k / epsilon) queries, our result shows that adaptivity enables polynomial savings in query complexity for junta testing.
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs:2017:7528,
author = {Xi Chen and Rocco A. Servedio and Li-Yang Tan and Erik Waingarten and Jinyu Xie},
title = {{Settling the Query Complexity of Non-Adaptive Junta Testing}},
booktitle = {32nd Computational Complexity Conference (CCC 2017)},
pages = {26:1--26:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-040-8},
ISSN = {1868-8969},
year = {2017},
volume = {79},
editor = {Ryan O'Donnell},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7528},
URN = {urn:nbn:de:0030-drops-75283},
doi = {10.4230/LIPIcs.CCC.2017.26},
annote = {Keywords: property testing, juntas, query complexity}
}
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Keywords: |
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property testing, juntas, query complexity |
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Collection: |
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32nd Computational Complexity Conference (CCC 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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01.08.2017 |
