Though it is unable to prove the majority is stablest conjecture, some partial results are enough to imply that MAX-CUT is hard to (3/4 + 1/(2/spl pi/) + /spl epsi/)-approximate (/spl ap/ .909155), assuming only the unique games conjecture.Expand

An invariance principle for multilinear polynomials with low influences and bounded degree is proved; it shows that under mild conditions the distribution of such polynmials is essentially invariant for all product spaces.Expand

This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.Expand

The algorithm and analysis exploit new structural properties of Boolean functions and obtain the first polynomial factor improvement on the naive n-k time bound which can be achieved via exhaustive search.Expand

A very easy proof that the randomized query complexity of nontrivial monotone graph properties is at least/spl Omega/(v/sup 4/3//p/sup 1/3/), where v is the number of vertices and p /spl les/ 1/2 is the critical threshold probability.Expand

The “optimal” lower bound for Locality-Sensitive Hashing (LSH) must be at least 1/<i>c</i> (minus <i>o</i><sub>d</sub>(1) is shown, following almost immediately from the observation that the noise stability of a boolean function at time <i-t</i) is a log-convex function of <i*t</ i.Expand

For any constant deletion rate 0 < Ω < 1, a mean-based algorithm is given that uses exp(O(n1/3) time and traces; it is proved that any mean- based algorithm must use at least exp(Ω(n 1/3)) traces; and a surprising result is found: for deletion probabilities δ > 1/2, the presence of insertions can actually help with trace reconstruction.Expand

We give the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution to within any constant error parameter. We also give the first… Expand

This paper addresses the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w · x - θ) by giving an algorithm that distinguishes halfspaces from functions that are e-far from any halfspace using only poly(1/e) queries, independent of the dimension n.Expand

Gaussian surface area essentially characterizes the computational complexity of learning under the Gaussian distribution, and this is the first subexponential time algorithm for learning general convex sets even in the noise-free (PAC) model.Expand