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Is there any Boolean function from $\{-1,1\}^n$ to $\{-1,1\}$ such that whose noise sensitivity is greater than delta, where Delta is the probability of each bit is flipped in n-tupple.

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Define noise sensitivity, please?.. I want to help, but I don't understand the question without definitions =) quick googling leads to ear problem descriptions, so I tried, but I can't find something standard that fits your description. – Patrick Da Silva Sep 23 '12 at 17:12
I don't at all understand your definition of Delta. – Yury Sep 23 '12 at 17:45

Take a look at Ryan O'Donnell's work, especially his PhD thesis on the noise sensitivity of Boolean functions:

You may also want to take a look at his blog on Boolean functions:

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