Minimum number of holes in unavoidable sets of partial words of size three

Authors:
Francine Blanchet-Sadri;Bob Chen;Aleksandar Chakarov
Affiliations:
Department of Computer Science, University of North Carolina, Greensboro, NC;Department of Mathematics, University of California, San Diego, LaJolla, CA;Department of Computer Science, University of Colorado at Boulder, Boulder, CO
Venue:
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Year:
2010

Citing 9
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Abstract

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. In this paper, 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.