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 ...
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
Let f be an integer valued function on a finite set V . We call an undirected graph G(V, E) a neighborhood structure for f. The problem of finding a local minimum for f can be phr...
We study the complexity of approximating the smallest eigenvalue of −∆ + q with Dirichlet boundary conditions on the d-dimensional unit cube. Here ∆ is the Laplacian, and th...
Given a Boolean function f, we study two natural generalizations of the certificate complexity C (f): the randomized certificate complexity RC (f) and the quantum certificate comp...