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Boolean Functions With Low Average Sensitivity Depend On Few Coordinates
1998
Combinatorica
Consider a function f : f0;1g n ! f0;1g. The sensitivity of a point v 2 f0;1g n is jfv 0 : f (v 0 ) 6 = f (v); dist(v; v 0 ) = 1gj, i.e. the number of neighbors of the point in the discrete cube on which the value of f di ers. The average sensitivity of f is the average of the sensitivity of all points in f0;1g n . (This can also be interpreted as the sum of the in uences of the n variables on f , or as a measure of the edge boundary of the set which f is the characteristic function of.) We
doi:10.1007/pl00009809
fatcat:pdidydm3uvaplazrivhp7jqswq