8 quotes
In this paper I deal only with automatic machines, and will therefore often omit the prefix ɑ-.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
The machine may also change the square which is being scanned, but only by shifting it one place to right or left.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol".
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
In some of the configurations in which the scanned square is blank... the machine writes down a new symbol on the scanned square: in other configurations it erases the scanned symbol.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q1, q2, ..., qK which will be called " m-configurations ".
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configuration the machine can effectively remember some of the symbols which it has "seen" (scanned) previously.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)
If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine.
On Computable Numbers, with an Application to the Entscheidungsproblem (1936)