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Degree and Sensitivity: tails of two distributions
[article]

2016
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arXiv
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pre-print

The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-s Boolean function can be computed by a polynomial over the reals of degree poly(s). The best known upper bounds on degree, however, are exponential rather than polynomial in s. Our main result is an approximate version of the conjecture: every Boolean function with

arXiv:1604.07432v1
fatcat:rb7puf3tbfftphxyou4tc2karu