Corpus ID: 5826640

Noise-Resistant Boolean-Functions are Juntas

@inproceedings{Kindler2003NoiseResistantBA,
  title={Noise-Resistant Boolean-Functions are Juntas},
  author={Guy Kindler and S. Safra},
  year={2003}
}
We consider Boolean functions over n binary variables, and the p-biased product measure over the inputs. We show that if f is of low-degree, that is, if its weight on Walsh products of size larger than k is small, then f is close to a junta, namely to a function which depends only on very small number of variables, independent of n. We conclude that any highly noise-resistant Boolean function must be a junta. Furthermore, we utilize our results to prove a switching lemma, one which may prove… Expand
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