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:
“A book is a part of life, a manifestation of life, just as much as a tree or a horse or a star. It obeys its own rhythms, its own laws, whether it be a novel, a play, or a diary. The deep, hidden rhythm of life is always there—that of the pulse, the heart beat.”
—Henry Miller (1891–1980)
“[How] the young . . . can grow from the primitive to the civilized, from emotional anarchy to the disciplined freedom of maturity without losing the joy of spontaneity and the peace of self-honesty is a problem of education that no school and no culture have ever solved.”
—Leontine Young (20th century)