How Many Holes Can an Unbordered Partial Word Contain?

Authors:
Francine Blanchet-Sadri;Emily Allen;Cameron Byrum;Robert Mercaş
Affiliations:
Department of Computer Science, University of North Carolina, Greensboro, USA NC 27402---6170;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA PA 15289;Department of Mathematics, University of Mississippi, USA MS 38677;GRLMC, Universitat Rovira i Virgili, Tarragona, Spain 43005
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

Citing 4
Cited 0

Partial words and a theorem of Fine and Wilf

Theoretical Computer Science
Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)

Algorithmic Combinatorics on Partial Words (Discrete Mathematics and Its Applications)
Unbordered partial words

Discrete Applied Mathematics
Primitive partial words

Discrete Applied Mathematics

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Abstract

Partial words are sequences over a finite alphabet that may have some undefined positions, or "holes," that are denoted by $\ensuremath{\diamond}$'s. A nonempty partial word is called bordered if one of its proper prefixes is compatible with one of its suffixes (here $\ensuremath{\diamond}$ is compatible with every letter in the alphabet); it is called unbordered otherwise. In this paper, we investigate the problem of computing the maximum number of holes a partial word of a fixed length can have and still fail to be bordered.