A non-linear time lower bound for Boolean branching programs

Abstract

We prove that for all positive integer k and for all sufficiently small /spl epsiv/>0 if n is sufficiently large then there is no Boolean (or 2-way) branching program of size less than 2/sup em/ which for all inputs X/spl sube/{0, 1, ..., n-1} computes in time kn the parity of the number of elements of the set of all pairs (x,y) with the property x/spl isin/X, y/spl isin/X, x0 is an absolute constant and n is sufficiently large with respect to /spl delta/.