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 Õ(k)/ 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 testin...

1 Deviation bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1 Markov and generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Class of sub-Gaussian random variables . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Basic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2....

We consider competitive algorithms for adaptive group testing problems. In the first part of paper, we develop an algorithm with constant c<1.452 thus improving up to now best known constants 1.5+ϵ from 2003. second part, prove nontrivial lower bound constants, namely that c is always larger than 1.31.