Computing regularities in strings

Regularities in strings model many phenomena and thus form the subject of extensive mathematical studies . Perhaps the most conspicuous regularities in strings are those that manifest themselves in the form of repeated subpatterns. In this paper, we study several forms of regularities of strings, that is, repeats, multirepeats, repetitions and runs. We present their similarities and differences by discussing their forms and properties and we explore the existing computation algorithms. We also discuss several data structures useful for computing regularities.