We consider the problem of testing functions for the property of being a k-junta (i.e., of depending on at most k variables). Fischer, Kindler, Ron, Safra, and Samorodnitsky (J. Comput. Sys. Sci., 2004) showed that \(\tilde{O}(k^2)/\epsilon\) queries are sufficient to test k-juntas, and conjectured that this bound is optimal for non-adaptive testing algorithms.

Our main result is a non-adaptive algorithm for testing k-juntas with \(\tilde{O}(k^{3/2})/\epsilon\) queries. This algorithm disproves the conjecture of Fischer et al.

We also show that the query complexity of non-adaptive algorithms for testing juntas has a lower bound of \(\min \big(\tilde{\Omega}(k/\epsilon), 2^k/k\big)\), essentially improving on the previous best lower bound of Ω(k).


Boolean Function Input Function Block Test Query Complexity Statistical Distance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Eric Blais
    • 1
  1. 1.Carnegie Mellon University 

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