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
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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