New and efficient approaches to the quasiperiodic characterisation of a string

A factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y; thus every cover u is also a border - both prefix and suffix - of y. A string y covered by u thus generalises the idea of a repetition; that is, a string composed of exact concatenations of u. Even though a string is coverable somewhat more frequently than it is a repetition, still a string that can be covered by a single u is rare. As a result, …