[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: rand("state")
From: |
Francesco Potorti` |
Subject: |
Re: rand("state") |
Date: |
Thu, 16 Feb 2006 18:41:38 +0100 |
>Thinking about it a little more - the entire pseudorandom sequence has a
>length of about 4*10^6001, so if you are making numerous sequences of
>length 10^9 say, the probability that two or more are overlapping is
>always extremely small (assuming that the starting point in the sequence
>is always selected at random from all possible starting points).
You just sent a calculation that can be used as the base to compute the
probability of having non-overlapping sequences, given the number of
sequences, their length, and the generator period, under the assumption
of uniformly choosing a random starting point for each sequence.
I did not check it, but yes, it can be seen as an instance of a birthday
problem.
Or else you can see it as this: have a generator of period P, from which
you have already taken N non-overlapping sequences of length L. The
probability that one more sequence of lenght L starting from a random
point does not overlap with one of the already taken N sequences is
equal to the probability that no taken sequence starts in an interval
of length 2*L, that is, (1-N/P)^(2*L), under the assumption that N*L<<P,
which is true in our case.
If what I wrote is correct, then you have the probability of choosing a
new good sequence, given that you have already chosen N.
--
Francesco Potortì (ricercatore) Voice: +39 050 315 3058 (op.2111)
ISTI - Area della ricerca CNR Fax: +39 050 313 8091
via G. Moruzzi 1, I-56124 Pisa Email: address@hidden
Web: http://fly.isti.cnr.it/ Key: fly.isti.cnr.it/public.key
-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------
- Re: rand("state"), (continued)
- Re: rand("state"), Mike Miller, 2006/02/15
- Re: rand("state"), Paul Kienzle, 2006/02/15
- Re: rand("state"), Mike Miller, 2006/02/15
- Re: rand("state"), Mike Miller, 2006/02/15
- Re: rand("state"), Francesco Potorti`, 2006/02/16
- Re: rand("state"), Paul Kienzle, 2006/02/16
- Re: rand("state"), Mike Miller, 2006/02/16
- Re: rand("state"), Paul Kienzle, 2006/02/16
- Re: rand("state"), Francesco Potorti`, 2006/02/16
- Re: rand("state"), Mike Miller, 2006/02/16
- Re: rand("state"),
Francesco Potorti` <=
- Re: rand("state"), Mike Miller, 2006/02/16
- Re: rand("state"), Francesco Potorti`, 2006/02/16
- Re: rand("state"), Michael Creel, 2006/02/17
- Re: rand("state"), Francesco Potorti`, 2006/02/17
- Re: rand("state"), Mike Miller, 2006/02/17
- Re: rand("state"), Francesco Potorti`, 2006/02/17
- Re: rand("state"), Mike Miller, 2006/02/17
- Re: rand("state"), Francesco Potorti`, 2006/02/17