From: couturie <couturie@carcariass.(none)>
Date: Wed, 18 Apr 2012 05:46:45 +0000 (+0200)
Subject: suite
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/turing4complexity.git/commitdiff_plain/19eb8563c27a0b70b252e940814dd379ff434074

suite
---

diff --git a/turing4complexity.tex b/turing4complexity.tex
index bbc2e69..2146039 100644
--- a/turing4complexity.tex
+++ b/turing4complexity.tex
@@ -19,7 +19,7 @@ blabalbabla
 In their paper, they introduced a method to compute the complexity of D(n).
 With D(4), 5 970 768 960 machines halt. There are 1832 different strings.
 
-\section{PRNG preserve distribution of short strings}
+\section{Property: a PRNG must preserve the distribution of short strings}
 
 In this section, we propose to measure the quality of a PRNG by considering that
 a good PRNG must preserve the distribution of short strings. More precisely, the
@@ -27,6 +27,16 @@ pseudo-random  numbers obtained  by a  PRNG can  form the  states of  the Rado's
 original  Busy Beaver. Then,  machines obtained  by such  a construction  can be
 executed and if the PRNG is good, machines should generate the same strings with
 the same distribution than the theoretical Busy Beaver (with all the enumeration
-of states).
+of states).  In  practice, PRNGs will not generate all  the strings with exactly
+the  same  probabilities. Nevertheless,  the  distance  between the  theoretical
+probabibilities and the obtained probabilities  with a PRNG is a good indication
+of the quality of the PRNG.
+
+In the following  we report our experiments. Let $S_i$ be  the string number $i$
+obtained by the busy beaver, $S(n)$ is the set of strings of $D(n)$. With $D(4)$
+there  are  1832  strings,  so  $|S(4)|=1832$.  $P_t(S_i)$  is  the  theoretical
+probability of  the string $S_i$ and  $P_{PRNG}(S_i)$ is the  probability of the
+string $S_i$  obtained with the execution of  a given PRNG. Let  For $D(n)$, the
+number of strings is
 
 \end{document}