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.
@InProceedings{gawrychowski_et_al:LIPIcs.STACS.2014.337, author = {Gawrychowski, Pawel and Manea, Florin and Nowotka, Dirk}, title = {{Testing Generalised Freeness of Words}}, booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)}, pages = {337--349}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-65-1}, ISSN = {1868-8969}, year = {2014}, volume = {25}, editor = {Mayr, Ernst W. and Portier, Natacha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.337}, URN = {urn:nbn:de:0030-drops-44694}, doi = {10.4230/LIPIcs.STACS.2014.337}, annote = {Keywords: Stringology, Pattern matching, Repetition, Pseudo-repetition} }
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