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Aug 2, 2012 at 3:12 comment added Igor Rivin @Brendan: I am well aware that most generators fail at least some of the tests. However, the "probably repeating after $2^{m/2}$ steps" statement is not so useful for $m=128,$ which is not such a big number.
Aug 2, 2012 at 2:43 history edited Brendan McKay CC BY-SA 3.0
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Aug 2, 2012 at 2:29 comment added Brendan McKay @Robert: Yes, and note that if the internal state was truly random it would repeat after about $2^{m/2}$ steps (birthday paradox). Most deterministic random number generators used in practice, except possibly for some very slow ones used for cryptographic applications, fail one of the many statistical tests when a huge but plausible amount of data is collected from them.
Aug 1, 2012 at 23:46 comment added Robert Israel The output of a pseudo-random generator whose state uses at most $m$ bits of memory is periodic after the first $2^m$ outputs, with period at most $2^m$, and this can be checked.
Aug 1, 2012 at 19:13 comment added Igor Rivin I am a bit puzzled by the "this is of course possible" statement. Is there some algorithm which, given some large number $N$ of pseudo-random numbers, can return "pseudo" with high probability?
Aug 1, 2012 at 18:32 comment added celine Thanks....reaching the conclusion that the sample is too small or that the generators are too random to determine anything is also valuable ...
Aug 1, 2012 at 13:56 history answered Brendan McKay CC BY-SA 3.0