Re: Random number generation using a 256-state cellular automaton

Vend wrote:



On 23 Gen, 21:01, Michael Olea <o...@xxxxxxxxxxxxx> wrote:

Hi, Tony. I did not see this post, since I was folowing the thread on
C.A.P.

The author didn't post there. Kent cross-posted

Anyway, I have a conjecture: two rule tables should yield the same
results on the Diehard tests if they have the same cycle structure. If
that's true, then the search space can be sharply reduced - instead of
256!*255! tables, down to P(256)*P(255), where P(N) is the number of
integer partitions of N.

What is an integer partition?

A partition of a positive number into summands. P(6) = 11:

1) 1+1+1+1+1+1 2) 1+1+1+1+2 3) 1+1+1+3 4) 1+1+4, 5) 1+2+2 6) 1+5
7) 1+2+3 8) 2+2+2 9) 2+4 10) 3+3 11) 6

P(256) is much smaller than 256!.

-- Michael


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