Unavoidable Sets of Partial Words of Uniform Length

Joey Becker
(Department of Mathematics, University of Nebraska)
F. Blanchet-Sadri
(Department of Computer Science, University of North Carolina)
Laure Flapan
(Department of Mathematics, Yale University)
Stephen Watkins
(Department of Mathematics, Vanderbilt University)

A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether or not a given finite set of n partial words over a k-letter alphabet is avoidable is NP-hard, even when we restrict to a set of partial words of uniform length. So classifying such sets, with parameters k and n, as avoidable or unavoidable becomes an interesting problem. In this paper, we work towards this classification problem by investigating the maximum number of holes we can fill in unavoidable sets of partial words of uniform length over an alphabet of any fixed size, while maintaining the unavoidability property.

In Erzsébet Csuhaj-Varjú, Pál Dömösi and György Vaszil: Proceedings 15th International Conference on Automata and Formal Languages (AFL 2017), Debrecen, Hungary, September 4-6, 2017, Electronic Proceedings in Theoretical Computer Science 252, pp. 26–40.
Published: 21st August 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.252.7 bibtex PDF
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