Structured programming, canonical structures: Per the Church-Turing thesis any algorithm can be computed by a model known to be Turing complete, and per Minsky's demonstrations Turing completeness requires only four instruction types — conditional GOTO, unconditional GOTO, assignment, HALT.

This extreme growth can be exploited to show that f, which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

To make a Turing machine that speaks Chinese, Searle gets in a room stocked with algorithms programmed to respond to Chinese questions, i. e., Turing machines, programmed to correctly answer in Chinese questions asked in Chinese, and he finds he's able to process the inputs to outputs perfectly without having any understanding of Chinese, nor having any idea what the questions and answers could possibly mean.

If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.

As a third issue, philosophers who dispute the validity of the Turing test may feel that it is possible, at least in principle, for verbal report to be dissociated from consciousness entirely: a philosophical zombie may give detailed verbal reports of awareness in the absence of any genuine awareness.

The field of recursion theory, meanwhile, categorizes undecidable decision problems by Turing degree, which is a measure of the noncomputability inherent in any solution.

Despite the language's intentionally obtuse and wordy syntax, INTERCAL is nevertheless Turing-complete: given enough memory, INTERCAL can solve any problem that a Universal Turing machine can solve.

In a deterministic Turing machine, the set of rules prescribes at most one action to be performed for any given situation.

Configurations and the yields relation on configurations, which describes the possible actions of the Turing machine given any possible contents of the tape, are as for standard Turing machines, except that the yields relation is no longer single-valued.

The notion of string acceptance is unchanged: a non-deterministic Turing machine accepts a string if, when the machine is started on the configuration in which the tape head is on the first character of the string ( if any ), and the tape is all blank otherwise, at least one of the machine's possible computations from that configuration puts the machine into a state in.

Equivalently, a problem is # P-complete if and only if it is in # P, and for any non-deterministic Turing machine (" NP machine "), the problem of computing its number of accepting paths can be reduced to this problem.

By a straightforward reduction to the halting problem it is possible to prove that ( for any Turing complete language ) finding all possible run-time errors in an arbitrary program ( or more generally any kind of violation of a specification on the final result of a program ) is undecidable: there is no mechanical method that can always answer truthfully whether a given program may or may not exhibit runtime errors.

It might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory.

So in principle, any problem that can be solved ( decided ) by a Turing machine can be solved by a computer that has a bounded amount of memory.

Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer.

A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine ( UTM, or simply a universal machine ).

Establishing the Loebner Prize, he introduced the Turing Test to a wider public, and stimulated interest in this science.

" Turing replies by saying that we have no way of knowing that any individual other than ourselves experiences emotions, and that therefore we should accept the test.

In his 1980 Turing Award lecture, C. A. R. Hoare described his experience in the design of ALGOL 60, a language that included bounds checking, saying:

Since NC contains NL, it is also unknown whether a space-efficient algorithm for computing the GCD exists, even for nondeterministic Turing machines.

To show that something is Turing complete, it is enough to show that it can be used to simulate the most primitive computer, since even the simplest computer can be used to simulate the most complicated one.

The features used to achieve Turing completeness can be quite different ; Fortran systems would use loop constructs or possibly even goto statements to achieve repetition ; Haskell and Prolog, lacking looping almost entirely, would use recursion.

Because of Savitch's theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a nondeterministic Turing machine without needing much more space ( even though it may use much more time ).

At a deeper level, CRM114 is also a string pattern matching language, similar to grep or even Perl ; although it is Turing complete it is highly tuned for matching text, and even a simple ( recursive ) definition of the factorial takes almost ten lines.

Fascinated by Alan Turing's imitation game, and considering creating a system himself to pass it, Loebner realised that even if he were to succeed in developing a computer that could pass the Turing test, no avenue existed in which to prove it.

Note that while these reductions are stronger in the sense that they provide a finer distinction into equivalence classes, and have more restrictive requirements than Turing reductions, this is because the reductions themselves are less powerful ; there may be no way to build a many-one reduction from one set to another even when a Turing reduction for the same sets exists.

John Backus presented FP in his 1977 Turing Award lecture " Can Programming Be Liberated From the von Neumann Style?

Subsequent formalizations were framed as attempts to define " effective calculability " or " effective method "; those formalizations included the Gödel – Herbrand – Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's " Formulation 1 " of 1936, and Alan Turing's Turing machines of 1936 – 7 and 1939.

It was not a Turing complete computer, which distinguishes it from more general machines, like contemporary Konrad Zuse's Z3 ( 1941 ), or later machines like the 1946 ENIAC, 1949 EDVAC, the University of Manchester designs, or Alan Turing's post-War designs at NPL and elsewhere.

We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.

Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus as the formal representation of algorithms.

" The Turing test simply extends this " polite convention " to machines.

And in a proof-sketch added as an " Appendix " to his 1936 – 37 paper, Turing showed that the classes of functions defined by λ-calculus and Turing machines coincided.

This was done by Alonzo Church in 1936 with the concept of " effective calculability " based on his λ calculus and by Alan Turing in the same year with his concept of Turing machines.

Turing reduced the halting problem for Turing machines to the.

It is still used in the area of computability theory, although Turing machines are arguably the preferred model for computation.

Alternatively, NP can be defined using deterministic Turing machines as verifiers.

In particular, nondeterministic Turing machines are equivalent with deterministic Turing machines.

However, what worries me about what I just said is that some people would think of Turing machines and Goedel's theorem as fundamentals.

" Since the words " think " and " machine " can't be defined in a clear way that satisfies everyone, Turing suggests we " replace the question by another, which is closely related to it and is expressed in relatively unambiguous words.

" In other words, Turing is no longer asking whether a machine can " think "; he is asking whether a machine can act indistinguishably from the way a thinker acts.

* A computer will pass the Turing test by the last year of the decade ( 2029 ), meaning that it is a Strong AI and can think like a human ( though the first A. I.

For example, that a Watt governor is a better metaphorical description of the way humans think than a Turing machine style computer.