Abstract
The notion of an unavoidable set of words appears frequently in the fields of mathematics and theoretical computer science, in particular with its connection to the study of combinatorics on words. The theory of unavoidable sets has seen extensive study over the past twenty years. In this paper we extend the definition of unavoidable sets of words to unavoidable sets of partial words. Partial words, or finite sequences that may contain a number of “do not know” symbols or holes, appear in natural ways in several areas of current interest such as molecular biology, data communication, DNA computing, etc. We demonstrate the utility of the notion of unavoidability on partial words by making use of it to identify several new classes of unavoidable sets of full words. Along the way we begin work on classifying the unavoidable sets of partial words of small cardinality. We pose a conjecture, and show that affirmative proof of this conjecture gives a sufficient condition for classifying all the unavoidable sets of partial words of size two. Lastly we give a result which makes the conjecture easy to verify for a significant number of cases.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–0452020. A World Wide Web server interface at www.uncg.edu/mat/research/unavoidablesets has been established for automated use of the program. We thank the referees of preliminary versions of this paper for their very valuable comments and suggestions.
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Blanchet-Sadri, F., Brownstein, N.C., Palumbo, J. (2007). Two Element Unavoidable Sets of Partial Words. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_12
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DOI: https://doi.org/10.1007/978-3-540-73208-2_12
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