Motivated by recent revelations of widespread state surveillance of personal communication,
many solutions now claim to offer secure and private messaging. This includes both a large …

Representations of Boolean functions by real polynomials play an important role in
complexity theory. Typically, one is interested in the least degree of a polynomial p (x_1 …

The communication complexity of a function f (x, y) measures the number of bits that two
players, one who knows x and the other who knows y, must exchange to determine the …

The sign-rank of a matrix A=A_ij with \pm1 entries is the least rank of a real matrix B=B_ij
with A_ijB_ij>0 for all i,j. We obtain the first exponential lower bound on the sign-rank of a …

We prove a general memory-samples lower bound that applies for a large class of learning
problems and shows that for every problem in that class, any learning algorithm requires …

We develop a new method to prove communication lower bounds for composed functions of
the form f∘g^n, where f is any boolean function on n inputs and g is a sufficiently “hard” two …

We prove several results which, together with prior work, provide a nearly-complete picture
of the relationships among classical communication complexity classes between PP and …

We develop a new method to prove communication lower bounds for composed functions of
the form fo gn where f is any boolean function on n inputs and g is a sufficiently" hard" two …

The sign-rank of a matrix A with±1 entries is the smallest rank of a real matrix with the same
sign pattern as A. To the best of our knowledge, there are only three known methods for …

The threshold degree of a Boolean function f\!\!\,:{0,1\}^n→{-1,+1\} is the least degree of a
real polynomial p such that f(x)≡\rmsgn\,p(x). We construct two halfspaces on {0,1\}^n …