We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We ...
We describe a quantum black-box network computing the majority of N bits with zerosided error using only 2 3 N + O( N log( -1 log N)) queries: the algorithm returns the correct an...
Thomas P. Hayes, Samuel Kutin, Dieter van Melkebee...
We study the problem of local search on a graph. Given a real-valued black-box function f on the graph's vertices, this is the problem of determining a local minimum of f--a v...
We present several results on the complexity of various forms of Sperner’s Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over ...
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...