Large-Scale Studies of the Repetition Characteristic for Different Models of Symbolic Sequences

Using a standard suffix-tree algorithm, we study the repetition characteristic
$v(t)$
, which has been introduced by F. Golcher, for different models of random symbolic sequences and compare it with the corresponding data obtained for natural-language texts and program codes. The character of
$v(t)$
function, the saturated repetition parameter
$v_{0}$
averaged at large enough times
$t$
and the appropriate standard deviation
$\Delta v_{0}$
are examined for 144 natural, random and randomized texts of different types. The main peculiarities of repetitions peculiar for the Simon, Markov and Miller's monkey text-generating models are analyzed. The results obtained for these analytically tractable models can be useful for developing mathematical fundamentals of the repetition characteristic.