Sentences with phrase «turing machines»

Jacob Aron says that if one of the Turing machines simulated by Adam Yedidia and Scott Aaronson halts, it would prove the set of axioms of mathematics called ZFC to be inconsistent, but mathematicians wouldn't be too panicked because «they could simply shift to a slightly stronger set of axioms» (14 May, p 9).

Jacob Aron says that if one of the Turing machines simulated by Adam Yedidia and Scott Aaronson halts, it would...

Turing machines differ from automobiles and other kinds of machines in that they are designed specifically to manipulate the symbols of some finite alphabet.

The halting problem entails that for any effective scheme that can decide whether Turing machines halt or not, there exists a Turing machine more complex than the scheme — hence the scheme (or a Turing machine constructed from the scheme) will not necessarily be able to decide its action.

Second, major recent developments in mathematics, logic, and computer science have shown an exact relationship between certain logical notions and Turing machines.

Most ordinary machines can function (in part) as Turing machines if there is some way to identify symbolically their input from the environment and their output to the environment.

The reasons for choosing Turing machines are twofold.

We understand very well the effective, and almost intelligent, power that Turing machines can have through their current use as computers.

Both, however, may be interpreted in terms of Turing machines.

In a certain technical sense (explained later), there is no limit to the complexity of the interaction of Turing machines with their environment.

Since the goal of this paper is to describe a mechanistic model of explanation, the connection between these logical notions and Turing machines will allow us to establish the relationship between the explanatory model and the image of the machine.

The remarkable thing about Turing machines as proposed in their original archaic form is what can be proved about them.

If the Turing Machine hadn't been invented, would we still be in the midst of today's computing revolution?

This would mean that an abstract Turing machine defined by us could not have a complete representation of a human feeling.

This universal Turing machine reads as part of its input data the Turing machine table of the duplicated machine and takes whatever action this machine would have taken on its appropriate input data.

The internal relations of a Turing machine would have to be similarly complex constructs of the basic alphabet and vocabulary of the machine.

It is much easier today to build a digital computer which can function as a Turing machine.

What would it mean to understand a Turing machine to have such internal relations?

The hardware acting as a universal Turing machine is adequate.

It is the that each line of a Turing machine table, that fixed structure that determines the nature of the Turing machine, can be considered to be a simple mechanical structure or action on which the complex structure of the machine depends.

A Turing machine in its simplest characterization is a self - contained entity that gives symbolic output information in response to symbolic input information.

For example, an automobile may act as a Turing machine as it determines a new direction of travel from the angle of the steering wheel and its current direction.

He proved that there can not exist a Turing machine which can decide in all cases whether an arbitrary Turing machine will halt or not when given an arbitrary input.

Nevertheless, since the possibilities of grouping the Turing machine's primitive table into higher level concepts are quite varied, a new philosophy of mechanism would tend to support an organization of software into a higher level language that is intuitively mechanical.

All right, life originated when information began to move in a system that could remember and modify its own state — life is a Turing machine.

First, a Turing machine is precisely defined.

A model that is well defined by effective procedures may be translated by the authority of Church's thesis into a Turing machine that captures the structure of the model.

Alan Turing invented the Turing machine as an intellectual tool in the 1930's in order to solve problems in mathematics.

This confirms to me only that they do not appreciate the levels of complexity possible in contemporary machines and in particular in a universal Turing machine.

A constructed Turing machine that represents a set of well defined axioms and effective procedures would accept input information (appropriately coded) and give the entailed consequences in its output information — the same consequences that would be obtained by using the logical procedures on the axioms.

Turing himself proved that a single Turing machine can be constructed which can reproduce the action of any Turing machine whatsoever.

But to attempt to analyze the function of a complex Turing machine by examining each of the individual lines of its table would be extremely difficult.

But clearly a Turing machine can be constructed as a machine, and must be considered as a machine.

The exactly determined behavior of the Turing machine, however, is conditioned upon its environment.

The complete action of a Turing machine, in response to its input information, is controlled by the lines in its fixed table each of which has four entries: the current state, the symbol read, the action to be taken, and the new state.

As normally understood, a classical Turing machine reads one symbol at a time, and in terms of its current state and the symbol read takes an action, which may be to erase, print a new symbol, or move to the right or left one space, after which it goes to a new (or the same) state.

First, we would have to understand a Turing machine to be identified not only with its fixed table, but also with its input and output information.

If however, the higher level concepts are clearly defined by effective procedures, they may then be subdivided into component parts, which parts may also then be subdivided until we finally reach very simple actions that can be described by lines of a Turing machine table.

A Turing machine would then not only include a part of its environment but would be both constituted by its environment as well as constituted by its reaction to its environment.

An explanation will be considered mechanical if it can be transformed without loss of information, literally, into a Turing machine.

There are technical ways of translating the axioms and laws of transformation in logic into a Turing machine that will do the same thing that can be done with the axioms through the logical laws of transformation.

Church's thesis entails that any algorithm (well defined procedure that eventually terminates) may be translated without loss of information into a Turing machine.

While the layperson may now be most familiar with Turing's work on Enigma and the later test that bears his name, Turing's most important mathematical contribution is his 1936 paper «On Computable Numbers,» which introduced the famous Turing machine.

Wolfram Research Hey, remember that $ 25,000 prize awarded by software company Wolfram Research last week for identifying the simplest «universal» theoretical computer, or Turing machine?

A machine made of DNA offers a new concept for a non-deterministic universal Turing machine that could solve problems faster than existing computers

Turing provided an influential formalisation of the concept of the algorithm and computation with the Turing machine, formulating the now widely accepted «Turing» version of the Church - Turing thesis, namely that any practical computing model has either the equivalent or a subset of the capabilities of a Turing machine.

I am always amazed to hear comments like «reduce calories and increase exercise to control your obesity» Correct me if I am wrong but as far as I know science has not discovered a «free will» organ in the body... and before you say the brain, remember that as far as neuro - scientists know it is just a very complex turing machine.

The Turing machine is an abstract machine, not a particular one.

is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input.

But the ordinary use of this kind of hardware — the programming of it — is a literary art, just because all of the Turing machine, the operations, and the program are abstractions.