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.