The collision problem is to decide whether a function X : {1, . . . , n} {1, . . . , n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of...
We convert cell-probe lower bounds for polynomial space into stronger lower bounds for near-linear space. Our technique applies to any lower bound proved through the richness meth...
Linearity tests are randomized algorithms which have oracle access to the truth table of some function f, and are supposed to distinguish between linear functions and functions whi...
A strong direct product theorem (SDPT) states that solving n instances of a problem requires ˝.n/ times the resources for a single instance, even to achieve success probability 2 ...
We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circui...