A generalization of Thue freeness for partial words

Authors:
F. Blanchet-Sadri;Robert Merca;Geoffrey Scott
Affiliations:
Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 274026170, USA;Research Group on Mathematical Linguistics, Rovira i Virgili University, Pl. Imperial Tàrraco 1, Tarragona 43005, Spain;Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, NH 03755, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

This paper approaches the combinatorial problem of Thue freeness for partial words. Partial words are sequences over a finite alphabet that may contain a number of ''holes''. First, we give an infinite word over a three-letter alphabet which avoids squares of length greater than two even after we replace an infinite number of positions with holes. Then, we give an infinite word over an eight-letter alphabet that avoids longer squares even after an arbitrary selection of its positions are replaced with holes, and show that the alphabet size is optimal. We find similar results for overlap-free partial words.