Turing had the idea now called a Turing machine. It was his exact formalization of a what had informally been described by expressions such as 'effective method'. Turing argued that his formalism was sufficiently general to encompass anything that a human being could do when carrying out a definite method.
The Turing machine concept involves specifying a very restricted set of logical operations, but Turing showed how other more complex mathematical procedures could be built out of these atomic components.
A Turing machine is an abstract representation of a computing device. It consists of a read/write head that scans a (possibly infinite) one-dimensional (bi-directional) tape divided into squares, each of which is inscribed with a 0 or 1. Computation begins with the machine, in a given "state", scanning a square. It erases what it finds there, prints a 0 or 1, moves to an adjacent square, and goes into a new state. This behavior is completely determined by three parameters: (1) the state the machine is in, (2) the number on the square it is scanning, and (3) a table of instructions. The table of instructions specifies, for each state and binary input, what the machine should write, which direction it should move in, and which state it should go into. (E.g., "If in State 1 scanning a 0: print 1, move left, and go into State 3".) The table can list only finitely many states, each of which becomes implicitly defined by the role it plays in the table of instructions. These states are often referred to as the "functional states" of the machine.
A Turing machine, therefore, is more like a computer program (software) than a computer (hardware). Any given Turing machine can be realized or implemented on an infinite number of different physical computing devices. Computer scientists and logicians have shown that if conventional digital computers are considered in isolation from random external inputs (such as a bit stream generated by radioactive decay), then given enough time and tape, Turing machines can compute any function that any conventional digital computer can compute. Also, a ‘probabilistic automaton’ can be defined as a Turing machine in which the transition from input and state to output and state takes place with a certain probability (E.g. "If in State 1 scanning a 0: (a) there is a 60% probability that the machine will print 1, move left, and go into State 3, and (b) there is a 40% probability that the machine will print 0, move left, and go into State 2".)
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