Testing Generalised Freeness of Words

Authors Pawel Gawrychowski, Florin Manea, Dirk Nowotka

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Pawel Gawrychowski
Florin Manea
Dirk Nowotka

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Pawel Gawrychowski, Florin Manea, and Dirk Nowotka. Testing Generalised Freeness of Words. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 337-349, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


Pseudo-repetitions are a natural generalisation 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 (anti-/morphism, for short). We approach the problem of deciding efficiently, for a word w and a literal anti-/morphism f, whether w contains an instance of a given pattern involving a variable x and its image under f, i.e., f(x). Our results generalise both the problem of finding fixed repetitive structures (e.g., squares, cubes) inside a word and the problem of finding palindromic structures inside a word. For instance, we can detect efficiently a factor of the form xx^Rxxx^R, or any other pattern of such type. We also address the problem of testing efficiently, in the same setting, whether the word w contains an arbitrary pseudo-repetition of a given exponent.
  • Stringology
  • Pattern matching
  • Repetition
  • Pseudo-repetition


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