Random

[Pfoertner, Hugo]

-----Ursprüngliche Nachricht-----
Von: y.kohmoto [mailto:zbi74583 at boat.zero.ad.jp] 
Gesendet: Freitag, 18. Juni 2004 07:17
An: seqfan at ext.jussieu.fr
Betreff: Random

    Hello, seqfans.
    Is there  anyone who is an expert of random sequence?
    Tell me a good definition of " random sequence" and a definition of
"good random sequence".

    Yasutoshi

The topic "what is random" has been exhaustively discussed in NGs sci.math,
sci.crypt, comp.compression, etc. A lot of material on (Pseudo-)Random
numbers
can be found in D. Knuth's TAOCP (Vol. 2?).

If you look at applications, I would say: A good random sequence is
something that
passes G. Marsaglias "DIEHARD" tests:

DIEHARD: a battery of tests for random number generators developed by George
Marsaglia
http://stat.fsu.edu/~geo/diehard.html

More information:
Scientific Computing FAQ: Random Number Generators (RNGs)
http://www.mathcom.com/corpdir/techinfo.mdir/scifaq/q210.html

Some people think "true" random sequences can only be generated by physical
processes
like turbulence, radioactive decay, thermal noise, quantum noise, etc. All
such sources need some
post-processing if their output has to pass a test battery like DIEHARD.
Links to physical
RNGs can be found in:
http://world.std.com/~reinhold/truenoise.html

Moer links in
RANDOM NUMBERS and MONTE CARLO METHODS
http://random.mat.sbg.ac.at/links/crypto.html

Hugo Pfoertner