In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem X a successively harder decision problem X ′ with the property that X ′ is not decidable by an oracle machine with an oracle for X.
The operator is called a jump operator because it increases the Turing degree of the problem X. That is, the problem X ′ is not Turing reducible to X. Post's theorem establishes a relationship between the Turing jump operator and the arithmetical hierarchy of sets of natural numbers. Informally, given a problem, the Turing jump returns the set of Turing machines which halt when given access to an oracle that solves that problem.
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