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 …

Any proof of P≠ NP will have to overcome two barriers: relativization and natural proofs. Yet
over the last decade, we have seen circuit lower bounds (eg, that PP does not have linear …

A Brief Introduction to Fourier Analysis on the Boolean Cube Page 1 Theory OF Computing
Library Graduate Surveys, TCGS 1 (2008), pp. 1–20 http://theoryofcomputing.org A Brief …

The general adversary bound is a semi-definite program (SDP) that lower-bounds the
quantum query complexity of a function. We turn this lower bound into an upper bound, by …

In a breakthrough result, Razborov (2003) gave optimal lower bounds on the communication
complexity of every function f of the form f (x, y)= D (| x AND y|) for some D:{0, 1,..., n}->{0, 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 …

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 approximate degree of a Boolean function f is the least degree of a real polynomial that
approximates f pointwise to error at most 1/3. The approximate degree of f is known to be a …

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 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 …