Definition
Given two sets of natural numbers, we say is Turing reducible to and write
if there is an oracle machine that computes the characteristic function of A when run with oracle B. In this case, we also say A is B-recursive and B-computable.
If there is an oracle machine that, when run with oracle B, computes a partial function with domain A, then A is said to be B-recursively enumerable and B-computably enumerable.
We say is Turing equivalent to and write if both and The equivalence classes of Turing equivalent sets are called Turing degrees. The Turing degree of a set is written .
Given a set, a set is called Turing hard for if for all . If additionally then is called Turing complete for .
Read more about this topic: Turing Reduction
Famous quotes containing the word definition:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)