We study differential privacy in a distributed setting where two parties would like to perform
analysis of their joint data while preserving privacy for both datasets. Our results imply …

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 …

The primary goal of this paper is to define and study the interactive information complexity of
functions. Let f (x, y) be a function, and suppose Alice is given x and Bob is given y …

We show a power 2.5 separation between bounded-error randomized and quantum query
complexity for a total Boolean function, refuting the widely believed conjecture that the best …

We construct a simple and total Boolean function F= f○ XOR on 2 n variables that has only
O (√ n) spectral norm, O (n 2) approximate rank, and O (n 2.5) approximate nonnegative …

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 show that almost all known lower bound methods for communication complexity are also
lower bounds for the information complexity. In particular, we define a relaxed version of the …

In STOC 1999, Raz presented a (partial) function for which there is a quantum protocol
communicating only O (log n) qubits, but for which any classical (randomized, bounded …

The Communication Complexity of Gap Hamming Distance Page 1 Theory OF Computing,
Volume 8 (2012), pp. 197–208 www.theoryofcomputing.org The Communication Complexity of …

We show an exponential gap between communication complexity and information
complexity, by giving an explicit example for a communication task (relation), with …