Number of holes in unavoidable sets of partial words I

Authors:
F. Blanchet-Sadri;Bob Chen;Aleksandar Chakarov
Affiliations:
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;Department of Computer Science, University of Colorado at Boulder, 430 UCB, Boulder, CO 80309-0430, USA
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem of fully characterizing all unavoidable sets of partial words of size three.