Repetitions in Empedokles

Two-Pattern Strings — Computing Repetitions & Near-Repetitions

In a recent paper we introduced infinite two-pattern strings on the alphabet {a, b} as a generalization of Sturmian strings, and we posed three questions about them: • Given a finite string x, can we in linear time O(|x|) recognize whether or not x is a prefix/substring of some infinite two-pattern string? • If recognized as two-pattern, can all the repetitions in x be computed in linear time? ...

Maximal repetitions in strings

The cornerstone of any algorithm computing all repetitions in strings of length n in O(n) time is the fact that the number of maximal repetitions (runs) is linear. Therefore, the most important part of the analysis of the running time of such algorithms is counting the number of runs. Kolpakov and Kucherov [FOCS’99] proved it to be cn but could not provide any value for c. Recently, Rytter [STA...

Weak Repetitions in Strings

A weak repetition in a string consists of two or more adjacent substrings which are permutations of each other. We describe a straightforward (n 2) algorithm which computes all the weak repetitions in a given string of length n deened on an arbitrary alphabet A. Using results on Fibonacci and other simple strings, we prove that this algorithm is asymptotically optimal over all known encodings o...

On Maximal Repetitions in Words

Discovering Hidden Repetitions in Words

Pseudo-repetitions are a natural generalization of the classical notion of repetitions in sequences: they are the repeated concatenation of a word and its encoding under a certain morphism or antimorphism. We approach the problem of deciding whether there exists an anti-/morphism for which a word is a pseudo-repetition. In other words, we try to discover whether a word has a hidden repetitive s...