Quantum information processing is the emerging field that defines and realizes computing
devices that make use of quantum mechanical principles such as the superposition …

Over the last twenty years, an exciting interplay has emerged between proof systems and
algorithms. Some natural families of algorithms can be viewed as a generic translation from …

We prove an optimal Ω (n) lower bound on the randomized communication complexity of the
much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially …

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 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 …

We show that deterministic communication complexity can be super logarithmic in the
partition number of the associated communication matrix. We also obtain near-optimal …

We use critical block sensitivity, a new complexity measure introduced by Huynh and
Nordström (STOC 2012), to study the communication complexity of search problems. To …

For any n-bit boolean function f, we show that the randomized communication complexity of
the composed function fog n, where g is an index gadget, is characterized by 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 …