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Adaptivity Helps for Testing Juntas

Authors Rocco A. Servedio, Li-Yang Tan, John Wright

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  • Property testing
  • juntas
  • adaptivity

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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.

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Rocco A. Servedio, Li-Yang Tan, and John Wright. Adaptivity Helps for Testing Juntas. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 264-279, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CCC.2015.264

Author Details

Rocco A. Servedio
Li-Yang Tan
John Wright

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