Ability of a computing system to simulate Turing machines
For the usage of this term in the theory of relative computability by oracle machines, see Turing reduction.
In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine[citation needed] (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete.[citation needed]
A related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P.[citation needed] The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing machine. A universal Turing machine can be used to simulate any Turing machine and by extension the purely computational aspects of any possible real-world computer.[citation needed]
To show that something is Turing-complete, it is enough to demonstrate that it can be used to simulate some Turing-complete system. No physical system can have infinite memory, but if the limitation of finite memory is ignored, most programming languages are otherwise Turing-complete.[citation needed]
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Programming, New Age International, 2007, ISBN 81-224-1379-X, p. 346 "TuringCompleteness". www.cs.odu.edu. Archived from the original on 16 August 2022. Retrieved...
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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...
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