Hidden subgroup problem: Let G be a group, X a finite set, and f : G → X a function that hides a subgroup H ≤ G. The function f is given via an oracle, which uses O(log |G|+log|X|) bits. Using information gained from evaluations of f via its oracle, determine a generating set for H.
A special case is when X is a group and f is a group homomorphism in which case H corresponds to the kernel of f.
Read more about Hidden Subgroup Problem: Motivation, Algorithms
Famous quotes containing the words hidden and/or problem:
“Art for art’s sake? I should think so, and more so than ever at the present time. It is the one orderly product which our middling race has produced. It is the cry of a thousand sentinels, the echo from a thousand labyrinths, it is the lighthouse which cannot be hidden ... it is the best evidence we can have of our dignity.”
—E.M. (Edward Morgan)
“The problem of culture is seldom grasped correctly. The goal of a culture is not the greatest possible happiness of a people, nor is it the unhindered development of all their talents; instead, culture shows itself in the correct proportion of these developments. Its aim points beyond earthly happiness: the production of great works is the aim of culture.”
—Friedrich Nietzsche (1844–1900)