How Many Holes Can an Unbordered Partial Word Contain?

@inproceedings{BlanchetSadri2009HowMH,
  title={How Many Holes Can an Unbordered Partial Word Contain?},
  author={Francine Blanchet-Sadri and Emily Allen and Cameron Byrum and Robert Mercas},
  booktitle={LATA},
  year={2009}
}
Partial words are sequences over a finite alphabet that may have some undefined positions, or “holes,” that are denoted by ’s. A nonempty partial word is called bordered if one of its proper prefixes is compatible with one of its suffixes (here 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. 
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