International Encyclopedia of Systems and Cybernetics

A digital machine with a supposedly unlimited data storage capacity, operating on one or more tapes each containing a numeral to produce a tape containing a numeral (After J. MYHILL, 1964, p.109).

D. RUELLE describes the machine as follows: "(It) has a finite muber of internal states: active states and a stop state. It does its work on an infinite ribbon, divided in a succession of squares (This ribbon serves as a memory). On each square on the ribbon a symbol, part of a finite alphabet, is written, one of these symbols being void. The TURING machine works by successive cycles, perfectly foreseable. If it is in the stop position, it does nothing. Otherwise, the machine reads the square it occupies and, according to its internal state and to what it just read, will do one of the following:

a) it will erase that which is written and write something else (Or the same thing) in the square;

b) it moves to the next square, to the left or to the right;

c) it changes to another internal state.

"If the new internal state is an active one, the machine will start a new cycle, according to the content of the new square and its new internal state.

"At the initial state, the ribbon contains a finite message, the data message (the rest of the ribbon is empty, i.e. made of squares marked with the void symbol). The machine starts at the beginning of the data message and … when it stops, it has written a new message, its answer or results message. The answer can be yes, or no, or possibly a number, or a longer message. It is possible to arrange a TURING machine to add or multiply whole numbers, or any other task that could be carried out by a computer".

In other words, the TURING machine is the universal theoretical model of the computer, in which an algorithm is used to process data, nothing more being needed.

RUELLE adds: "There is no need for an infinity of different machines for different tasks, because there exists a universal TURING machine. To operate a specific algorithm on this universal machine, one must describe on the ribbon a data message that contains at the same time the algorithm's description and the specific data that should be processed" (1991, p.181-2).

G. KLIR states that, according to the CHURCH-TURING thesis: "… a TURING machine is taken to be a precise formal equivalent of the intuitive notion of an algorithm" (G. KLIR, 1991, p.128).

As may be observed, these elements correspond to the computer program and the data store.

The unlimited storage capacity, which for example "would be required to multiply two arbitrary large numbers" (Ibid) is however a practical impossibility.

M. BUNGE rightly observes: "… TURING machines…, being equipped with infinitely long tapes, are strictly speaking unrealizable" (1977, p.33). They are a kind of thought experiment… which however led to the whole of computer technique.

E. VACCARI and M. D'AMATO put it in a different way, but the meaning is more or less similar: "In a dynamic perspective, the Turing machine might be considered as a special limiting case of a discrete time/discrete space model, where the time between state changes is of no significance"(2000, p. 175)