In this case it is called Turing equivalent.
Have computers finally passed the Turing test?
There are various equivalent formulations of the Church-Turing thesis.
The formal concept proposed by Turing was that of computability by Turing machine.
Roughly speaking, a UTM is a Turing machine that can mimic any other Turing machine.
More exactly, computable operations are those which can be effected by what Turing called automatic machines.
See the entry the Turing test for discussion of Block’s objection and other issues surrounding the Turing Test.
This allows infinitely accelerating Turing machines to compute functions, such as the halting function, that are Turing-uncomputable.
Turing argued that, given his various assumptions about human computers, the work of any human computer can be taken over by a Turing machine.
None of this can constitute objections to The Turing Test unless The Turing Test delivers necessary conditions for the attribution of intelligence.
A transformation of one Turing-uncomputable value into another Turing-uncomputable value is certainly a Turing-uncomputable operation.
As previously explained, Turing established the existence of real numbers that cannot be computed by standard Turing machines (Turing 1936).
But there are only countably many Turing machines; you can enumerate Turing machines by enumerating all lists of Turing machine instructions.
Essentially, then, the Church-Turing thesis says that no human computer, or machine that mimics a human computer, can out-compute the universal Turing machine.
According to the Church-Turing thesis (CTT), any function that is intuitively computable is computable by some Turing machine (i.e., Turing-computable).
The simulation thesis is much stronger than the Church-Turing thesis: as with the maximality thesis, neither the Church-Turing thesis properly so called nor any result proved by Turing or Church entails the simulation thesis.
The electronic stored-program digital computers for which the universal Turing machine was a blueprint are, each of them, computationally equivalent to a Turing machine, and so they too are, in a sense, models of human beings engaged in computation.
Even before Turing machines and all the other mathematical models of computation were proved equivalent, and before any statement of the Church-Turing thesis, Turing argued convincingly that his machines were as powerful as any possible computing device.
True enough, we think that there is a correct interpretation of exactly what test it is that is proposed by Turing (1950); but a complete discussion of the current standing of The Turing Test should pay at least some attention to the current standing of other tests that have been mistakenly supposed to be proposed by Turing (1950).
Bell’s Theorem | Church-Turing Thesis | computability and complexity | computational complexity theory | quantum mechanics | quantum mechanics: collapse theories | quantum mechanics: the role of decoherence in | quantum theory: philosophical issues in | quantum theory: quantum entanglement and information | quantum theory: the Einstein-Podolsky-Rosen argument in | Turing, Alan | Turing machines
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