In this paper we study some combinatorial properties of a class of languages that represent sets of words occurring in a text S up to some errors. More precisely, we consider sets of words that occur in a text S with k mismatches in any window of size r. The study of this class of languages mainly focuses both on a parameter, called repetition index, and on the set of the minimal forbidden words of the language of factors of S with errors. The repetition index of a string S is defined as the smallest integer such that all strings of this length occur at most in a unique position of the text S up to errors. We prove that there is a strong relation between the repetition index of S and the maximal length of the minimal forbidden words of the language of factors of S with errors. Moreover, the repetition index plays an important role in the construction of an indexing data structure. More precisely, given a text S over a fixed alphabet, we build a data structure for approximate string matching having average size O(|S|⋅logk+1|S|) and answering queries in time O(|x|+|occ(x)|) for any word x, where occ is the list of all occurrences of x in S up to errors.
|Data di pubblicazione:||2007|
|Titolo:||Languages with mismatches|
|Autori:||EPIFANIO C; GABRIELE A; MIGNOSI F; RESTIVO A; SCIORTINO M|
|Tipologia:||Articolo su rivista|
|Citazione:||EPIFANIO C, GABRIELE A, MIGNOSI F, RESTIVO A, & SCIORTINO M (2007). Languages with mismatches. THEORETICAL COMPUTER SCIENCE, 385, 152-166.|
|Digital Object Identifier (DOI):||10.1016/j.tcs.2007.06.006|
|Appare nelle tipologie:||01 - Articolo su rivista|