An Answer to a Conjecture on Overlaps in Partial Words Using Periodicity Algorithms

Authors:
Francine Blanchet-Sadri;Robert Mercaş;Abraham Rashin;Elara Willett
Affiliations:
Department of Computer Science, University of North Carolina, Greensboro, USA NC 27402---6170;GRLMC, Universitat Rovira i Virgili, Tarragona, Spain 43005;Department of Mathematics, Rutgers University, Piscataway, USA NJ 08854---8019;Department of Mathematics, Oberlin College, Oberlin, USA OH 44074-1019
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

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Abstract

We propose an algorithm that given as input a full word w of length n , and positive integers p and d , outputs (if any exists) a maximal p -periodic partial word contained in w with the property that no two holes are within distance d . Our algorithm runs in O (nd ) time and is used for the study of freeness of partial words. Furthermore, we construct an infinite word over a five-letter alphabet that is overlap-free even after the insertion of an arbitrary number of holes, answering affirmatively a conjecture from Blanchet-Sadri, Mercaş, and Scott.