Other Directory Sites: SeekWonder | Directory Owners Forum
The following archive was created by hippie-mail 7.98617-22 on Fri Aug 21 1998 - 17:20:38 ADT
Mike Rosing (eresrch@msn.fullfeed.com)
Sat, 18 Jul 1998 20:32:40 -0500 (CDT)
On Sat, 18 Jul 1998, Enzo Michelangeli wrote:
> "Pure whiteness" cannot be tested in a finite time, as this would require to
> compute the autocorrelation over an infinite interval. Over finite intervals
> which are not multiple of the period, all PRNG will show some discrepancy
> from constant autocorrelation (just like all RNG, no matter how good, over
> any interval).
Then the average autocorrelation should be zero over lots of intervals for
something "approaching" white asymptoticly.
> Besides, spectral tests (as any test based on estimates of the parameters of
> n-th order distributions) only spot a small subset of dependencies of each
> sample on the others, or on constant values. Most non-linear dependencies
> will escape such tests.
And if I can measure and characterize the non-linear dependencies using a
model of the source, what do I do with it? non-linear is usually "random",
what I'm looking for is random noise.
> So, you are in a _double_ state of sin: you think that algorithms can do
> better than real random generator! :-)
Algorithms massage real data, be they op amps or digitizers. Algorithms
for PRNG are not random at all, they can be tuned to pass any kind of
test for randomness one can think of. Real "randomness" is an untunable
signal, to be useful it must be outside our direct ability to control.
So I expect to see a difference. What's better depends on the task it's
to be used for.
> Actually, the entropy of a source cannot be "measured": you can only get
> (probabilistic!) upper bounds on it. This, often, also requires some
> assumptions on the generator. A simple example: no statistical test will
> ever tell you that "932384626433832" belongs to the (perfectly
> deterministic) decimal expansion of pi, as it actually does. If your suite
> had an ad-hoc test for "pi-ness detection" (supposing that it's feasible),
> it would still miss the sequences of digit of "e", or any other in the
> infinity of computable Borel numbers. Measurement is useful to ring alarms,
> but is no replacement for thoughtful design and (when available)
> mathematical proof.
What is a Borel number? The estimate of entropy can be done statisticly
like temperature, with enough data you can get the probability to within
some useful range. The math looks like it'll be fun.
Patience, persistence, truth,
Dr. mike
The following archive was created by hippie-mail 7.98617-22 on Fri Aug 21 1998 - 17:20:38 ADT