It has been suggested by some that a PRNG can be created that is -not-
repeating. There is a property of -all- RNG's that is called
k-distribution.
For a RNG to -be- a RNG it -must- be infinity-distributed. This means that
there are -no- string repititions -ever-. If this can't be guaranteed then
the algorithm can be a PRNG (there are other conditionals). A PRNG -by
definition- can -not- rule out repititions of some
very_large-distribution. Hence, -all- PRNG's must assume - even in
principle- some very_large-distribution sequence.
So, the statement "My PRNG has no modulus" is incorrect even in principle.
The Art of Computer Programming
Volume 2
Seminumerical Algorithms, 3ed
D.E. Knuth
ISBN 0-201-89684-2
Chapter 3 "Random Numbers"
Section 3.5 "What is a Random Sequence?"
He also has some things to say about Pi and its applicability as a seed
in this same section, and the assumptions that people make that are not
proven.
"The representation of of a positive real number n in the radix-b may be
regarded as a b-ary sequence; for example, pi corresponds to the 10-ary
sequence 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, ... People have
conjectured that this sequence is infinity-distributed, but nobody has yet
been able to prove it is even 1-distributed."
It's worth pointing out that the test of 'randomness' are -all'
statistical. They all have a margin of error. There is the a priori
recognition of 'window' effect.
Which gets to the reference I mentioned in one post about 'Garden of Eden'
sequences. These would be sequences that can -never- happen from -any- of
the given input states. It is a sequence of states the generator can not
make because they are outside the scope of its algorithm (there is usually
a data set independency assumed - you can be in -all- combinations of
start state). At least as far as I know this could apply to both (P)RNG's.
--
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The law is applied philosophy and a philosphical system is
only as valid as its first principles.
James Patrick Kelly - "Wildlife"
[EMAIL PROTECTED] www.ssz.com
[EMAIL PROTECTED] www.open-forge.org
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