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Suppose that one has a Blum–Shub–Smale machine. Is it possible to write down a program of finite length that produces a series of numbers, with each consisting of a finite number of digits, such that these numbers are truly random in the sense of Kolmogorov randomness, that is, no program of finite length on a Turing machine can produce the same series of numbers?

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    $\begingroup$ I don’t think so. Their Kolmogorov complexity would be logarithmic. $\endgroup$ – Yuval Filmus Apr 19 at 11:18

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