Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables ( see more at finite state machine, state transition table and control table ), as flowcharts ( see more at state diagram ), or as a form of rudimentary machine code or assembly code called " sets of quadruples " ( see more at Turing machine ).

Representations of algorithms can be classed into three accepted levels of Turing machine description:

:: "... prose used to define the way the Turing machine uses its head and the way that it stores data on its tape.

But Minsky shows ( as do Melzak and Lambek ) that his machine is Turing complete with only four general types of instructions: conditional GOTO, unconditional GOTO, assignment / replacement / substitution, and HALT.

He was highly influential in the development of computer science, giving a formalisation of the concepts of " algorithm " and " computation " with the Turing machine, which can be considered a model of a general purpose computer.

A model of computation may be defined in terms of an abstract computer, e. g., Turing machine, and / or by postulating that certain operations are executed in unit time.

* Alternating Turing machine, model of computation used in theoretical computer science

This is formalised by a human-assisted Turing machine.

The complexity of executing an algorithm with a human-assisted Turing machine is given by a pair, where the first element represents the complexity of the human's part and the second element is the complexity of the machine's part.

The complexity of solving the following problems with a human-assisted Turing machine is:

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.

Turing is widely considered to be the father of computer science and artificial intelligence.

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 >.

If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.

Among the famous mathematicians and cryptanalysts working there, the most influential and the best-known in later years was Alan Turing who is widely credited with being " The Father of Computer Science ".

In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of at most 1 / 3 for all instances.

This class is defined for a quantum computer and its natural corresponding class for an ordinary computer ( or a Turing machine plus a source of randomness ) is BPP.

" is too loaded with spurious connotations to be meaningful ; but he proposed to replace all such questions with a specific operational test, which has become known as the Turing test.

The Turing test is commonly cited in discussions of artificial intelligence as a proposed criterion for machine consciousness ; it has provoked a great deal of philosophical debate.

For example, Daniel Dennett and Douglas Hofstadter argue that anything capable of passing the Turing test is necessarily conscious, while David Chalmers argues that a philosophical zombie could pass the test, yet fail to be conscious.

Another way of putting the argument is to say computational computer programs can pass the Turing test for processing the syntax of a language, but that semantics cannot be reduced to syntax in the way Strong AI advocates hoped: processing semantics is conscious and intentional because we use semantics to consciously produce meaning by what we say.

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 the computer had passed the Turing test this way, it is fair, says Searle, to deduce that he would be able to do so as well, simply by running the program manually.

However, these causal properties can't be detected by anyone outside the mind, otherwise the Chinese Room couldn't pass the Turing test — the people outside would be able to tell there wasn't a Chinese speaker in the room by detecting their causal properties.

It can be visualized as a Turing machine with a black box, called an oracle, which is able to decide certain decision problems in a single operation.

An oracle Turing machine is a hypothetical device which, in addition to performing the actions of a regular Turing machine, is able to ask questions of an oracle, which is a particular set of natural numbers.

For example, supertasking Turing machines, under the usual assumptions, would be able to compute any predicate in the truth-table degree containing or.

This sometimes leads people to believe that eventually, computers will be able to solve any mathematical problem, no matter how complicated ( See Turing Test ).

Just as a Universal Turing machine can simulate any other Turing machine efficiently, so the universal quantum computer is able to simulate any other quantum computer with at most a polynomial slowdown.

In order to do this, Deutsch invents the notion of a CantGoTu environment ( named after Cantor, Gödel, and Turing ), using Cantor's diagonal argument to construct an ' impossible ' Virtual Reality which a physical VR generator would not be able to generate.

To see that this language is not recursively enumerable, imagine that we construct a Turing machine M which is able to give a definite answer for all such Turing machines, but that it may run forever on any Turing machine that does eventually halt.

The instructions are drawn from the two classes to form " instruction-sets ", such that an instruction set must allow the model to be Turing equivalent ( it must be able to compute any partial recursive function ).

Many different definitions of intelligence have been proposed ( such as being able to pass the Turing test ) but there is to date no definition that satisfies everyone.

Equivalently, there is a deterministic Turing machine M that runs in time O ( f ( n )) and is able to check a polynomial-length certificate for an input ; if the input is a " yes " instance, then at least one certificate is accepted, if the input is a " no " instance, no certificate can make the machine accept.

Using that information, scientists should be able to create simulated human brains inside of computers, leading to the first Artificial Intelligence ( a thinking computer capable of passing the Turing Test ) by 2029.

On this basis, the computer would be able to pass the Turing test despite the fact ( according to Block ) that it was not intelligent.

Consequently every programming language such as CPU level machine code, assembler, or any high level programming language has the same expressional power as the underlying Turing machine is able to compute.

Given unlimited resources, a classical computer can simulate an arbitrary quantum algorithm so quantum computation does not violate the Church – Turing thesis.

A Turing machine can simulate

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.

In computability theory, a system of data-manipulation rules ( such as 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 single-taped Turing machine.

Two computers P and Q are called Turing equivalent if P can simulate Q and Q can simulate P. Thus, a Turing-complete system is one that can simulate a Turing machine ; and, per the Church-Turing thesis, that any real-world computer can be simulated by a Turing machine, it is Turing equivalent to a Turing machine.

In colloquial usage, the terms " Turing complete " or " Turing equivalent " are used to mean that any real-world general-purpose computer or computer language can approximately simulate any other real-world general-purpose computer or computer language, within the bounds of finite memory – they are linear bounded automaton complete.