From: Achim Flammenkamp (achim@hrz.uni-bielefeld.de)
Date: Tue Apr 20 1993 - 10:00:35 UTC
In article <1qvied$i78@lll-winken.llnl.gov> dale@wente.llnl.gov (Dale M. Slone) writes:
>I have 2 question regarding random numbers:
>
>1) What statistical methods are appropriate to determine if 2 (or more)
> subsequences of random numbers are not correlated with each other.
> When I use rand() or rand48() I typically use <r*r>~.33333 and
^^^^^^^^^^^^ ???
Would does this mean (I expected <r*r>~length(r)/2 of a sequence "random" bits
> <r(i)*r(i+1)>~.250 as quick checks to establish that the individual
> sequences are random. This is for a massively parallel application.
>
>2) "Numerical Recipes" has a routine to generate random bits. My
> particular application could use random bit generation, but I
> would like to bias the mean, i.e. instead of <r>=.5, I would
> like to generate a sequence of bits such that <r>=.5+epsilon,
> where epsilon is a small number computed based on the problem
> size.
> Is there such a method, and how would I establish that the
> sequence is random?
Only a theoretical statement to your last question:
How to test whether a given sequence S of 0-1-digits is random or not ?
Assume there exists a function f(.,n) which is deterministic in the global
parameter list '.' and produces the n-th random digit of the (desired) sequence.
For allmost all random number generators in digital computers this is true.
Now, if you check the produced sequence S against it's generating function you
will have total correlation and should never call this a random sequence. So
you need special hardware like noicy diodes or "radioactive emitters" :(
Especial: By my definition, there are NO random sequences of finite length!
Ok. ---
What would I call a pseudo-random-sequence?
Each function g(.,n) which matches the random sequence S had about the same
complexity like f(.,n). Now it breaks down to an appropriate definition
of complexity of functions :>
But in practice you have even weaker conditions:
Replace "match" by "correlate to some(!) degree" and you must define how to
measure correlation of two (in)finite sequences. And the whole complexity
stuff follows once again.
achim
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