Autocorrelation On Words And Its Applications - Analysis of Suffix Trees by String-Ruler Approach

We study in a probabilistic framework some topics concerning the way words can overlap. Our probabilistic models assumes that a word is a sequence of i.i.d. symbols generated from a finite alphabet. This defines the so called Bernoulli model. We investigate the length of a subword that can be recopied, that is, a subword that occurs at least twice in a given word. An occurrence of such repeated substrings is easy to detect in a digital tree called a suffix tree. The length of a repeated substring corresponds to the typical depth in the associated suffix tree. Our main finding shows that the typical depth in a suffix tree is asymptotically distributed in the same manner as the typical depth in a digital tree that stores independent keys (i.e., independent tries). More precisely, we prove that the typical depth in a suffix tree built from the first n suffixes of a random word is normally distributed with the mean asymptotically becoming 1=h 1 log n and the variance ff \Delta log n, where..