[Math] Have anyone ever thought of continuous analog Turing machine

continuityturing-machines

Have anyone ever thought of continuous analog Turing machine? The machine adopts continuous (from R) the input data from the tape,
It moves to a different state depending on the value on the tape.
On the output tape Turing machine writes real numbers according to its program. Is it possible to construct a computer on these principles?

Best Answer

Yes. Quote:

Suppose, instead, we define a machine whose "state" at any time t is a real number s(t), and the "tape" is magnetized with intensity m(x) at location x (where x is the real-valued distance from the starting position). The machine is initially set to the state s(0) = 0 and placed at location x = 0 on the tape, which has been "programmed" with some initial profile of magnetic intensities over a finite range of the tape. (I'm treating m(x) as an ideal continuous function.)

About the question: "Is it possible to construct a computer on these principles?", analog computers were invented before the digital ones. The problem is that infinite resolution isn't more possible than infinite tape.

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