Timeline for How to test if two sets of random numbers might be from the same random number generator?
Current License: CC BY-SA 3.0
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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 |
add a reference
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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 |