One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix— th...
We study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a functi...
—We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most O(k3 log d). The previous best rank bound known was 2O(k2 ) (log d)k−2...
We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2−(...
We give polynomial time computable extractors for low-weight affince sources. A distribution is affine if it samples a random points from some unknown low dimensional subspace of ...