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

Abstract

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 v0 averaged at large enough times t and the appropriate standard deviation ∆v0 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 textgenerating models are analyzed. The results obtained for these analytically tractable models can be useful for developing mathematical fundamentals of the repetition characteristic.