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.
@InProceedings{chen_et_al:LIPIcs.CCC.2017.26, author = {Chen, Xi and Servedio, Rocco A. and Tan, Li-Yang and Waingarten, Erik and Xie, Jinyu}, 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 = {O'Donnell, Ryan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.26}, URN = {urn:nbn:de:0030-drops-75283}, doi = {10.4230/LIPIcs.CCC.2017.26}, annote = {Keywords: property testing, juntas, query complexity} }
Feedback for Dagstuhl Publishing