eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-06-06
264
279
10.4230/LIPIcs.CCC.2015.264
article
Adaptivity Helps for Testing Juntas
Servedio, Rocco A.
Tan, Li-Yang
Wright, John
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol033-ccc2015/LIPIcs.CCC.2015.264/LIPIcs.CCC.2015.264.pdf
Property testing
juntas
adaptivity