We discuss several complexity measures for Boolean functions: certi cate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. ...
Consider a two-party quantum communication protocol for computing some function f : {0, 1}n × {0, 1}n → Z. We show that the first message of P can be compressed to O(k) classi...
We describe a randomized algorithm that, given an integer a, produces a certificate that the integer is not a pure power of an integer in expected (log a)1+o(1) bit operations unde...
Abstract. We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Proble...
We consider the problem of bounded-error quantum state identification: given either state 0 or state 1, we are required to output `0', `1' or `?' ("don't ...
Dmitry Gavinsky, Julia Kempe, Oded Regev, Ronald d...