suite

diff --git a/turing4complexity.tex b/turing4complexity.tex
index bbc2e69263d2af70664803c6962b264002771743..21460399dc780fce7b943d895178dd110aec1dd0 100644 (file)
--- 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.
 
 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
 
 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
 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

 
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