In computability theory, a Turing reduction from a decision problem to a decision problem is an oracle machine that decides problem given an oracle for (Rogers 1967, Soare 1987). It can be understood as an algorithm that could be used to solve if it had available to it a subroutine for solving . The concept can be analogously applied to function problems.
If a Turing reduction from to exists, then every algorithm for [a] can be used to produce an algorithm for , by inserting the algorithm for at each place where the oracle machine computing queries the oracle for . However, because the oracle machine may query the oracle a large number of times, the resulting algorithm may require more time asymptotically than either the algorithm for or the oracle machine computing . A Turing reduction in which the oracle machine runs in polynomial time is known as a Cook reduction.
The first formal definition of relative computability, then called relative reducibility, was given by Alan Turing in 1939 in terms of oracle machines. Later in 1943 and 1952 Stephen Kleene defined an equivalent concept in terms of recursive functions. In 1944 Emil Post used the term "Turing reducibility" to refer to the concept.
Cite error: There are <ref group=lower-alpha> tags or {{efn}} templates on this page, but the references will not show without a {{reflist|group=lower-alpha}} template or {{notelist}} template (see the help page).
In computability theory, a Turingreduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine...
an elder brother, John Ferrier Turing, father of Sir John Dermot Turing, 12th Baronet of the Turing baronets. Turing's father's civil service commission...
language) Turing reductionTuring Robot, China Turing scheme Turing Street - A road in East London Turing switch Turing table Turing tarpit Turing test Computer...
Institute Turing Lecture Turing machine Turing patterns TuringreductionTuring switch Turing test Various institutions have paid tribute to Turing by naming...
computability (or recursive) theory, where it assumes the form of e.g. Turingreduction, but also in the realm of real-world computation in time (or space)...
of oracle Turing machines, as discussed below. The one presented here is from van Melkebeek (2003, p. 43). An oracle machine, like a Turing machine, includes:...
Church, Rózsa Péter, Alan Turing, Stephen Kleene, and Emil Post. The fundamental results the researchers obtained established Turing computability as the correct...
defining a new class GI, the set of problems with a polynomial-time Turingreduction to the graph isomorphism problem. If in fact the graph isomorphism...
combinations. Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. Its namesake,...
that T-reducibility relates to μ-recursiveness. Turingreduction Many-one reduction Truth-table reduction Arithmetical hierarchy Shoenfield, J. R. (July...
problem considered in Turing's 1936 paper ("does a Turing machine starting from a blank tape ever print a given symbol?"). However, Turing equivalence is rather...
therefore suffices to show that if limit computability is preserved by Turingreduction, as this will show that all sets computable from 0 ′ {\displaystyle...
Global Information
