Unbordered partial words

Authors:
F. Blanchet-Sadri;C. D. Davis;Joel Dodge;Robert Mercaş;Margaret Moorefield
Affiliations:
Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 27402-6170, USA;Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 27402-6170, USA;Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept 0112, LaJolla, CA 92093-0112, USA;GRLMC, Universitat Rovira i Virgili, Plaça Imperial Tárraco, 1, Tarragona, 43005, Spain and MOCALC Research Group, Faculty of Mathematics and Computer Science, University of Bucharest, A ...;Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 27402-6170, USA
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

An unbordered word is a string over a finite alphabet such that none of its proper prefixes is one of its suffixes. In this paper, we extend the results on unbordered words to unbordered partial words. Partial words are strings that may have a number of ''do not know'' symbols. We extend a result of Ehrenfeucht and Silberger which states that if a word u can be written as a concatenation of nonempty prefixes of a word v, then u can be written as a unique concatenation of nonempty unbordered prefixes of v. We study the properties of the longest unbordered prefix of a partial word, investigate the relationship between the minimal weak period of a partial word and the maximal length of its unbordered factors, and also investigate some of the properties of an unbordered partial word and how they relate to its critical factorizations (if any).