Repetitions in Text and Finite Automata 1

Abstract: A general way to find repetitions of factors in a given text is shown. We start with a classification of repetitions. The general models for finding exact repetitions in one string and in a finite set of strings are introduced. It is shown that d-subsets created during determinization of nondeterministic factor automata contain all information concerning repetitions of factors. The principle of the analysis of d-subsets is then used for finding approximate repetitions using several distances for a general finite alphabet and for an ordered alphabet including the case of presence of don’t care symbols. Complexity of finding repetitions is shown for exact repetitions in one string.