Abstract
In this paper, we investigate partial words, or finite sequences that may have some undefined positions called holes, of maximum subword complexity. The subword complexity function of a partial word w over a given alphabet of size k assigns to each positive integer n, the number p w (n) of distinct full words over the alphabet that are compatible with factors of length n of w. For positive integers n, h and k, we introduce the concept of a de Bruijn partial word of order n with h holes over an alphabet A of size k, as being a partial word w with h holes over A of minimal length with the property that \(p_w(n)=k^n\). We are concerned with the following three questions: (1) What is the length of k-ary de Bruijn partial words of order n with h holes? (2) What is an efficient method for generating such partial words? (3) How many such partial words are there?
This material is based upon work supported by the National Science Foundation under Grant No. DMS–0754154. The Department of Defense is also gratefully acknowledged. We thank the referees of preliminary versions of this paper for their very valuable comments and suggestions.
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Blanchet-Sadri, F., Schwartz, J., Stich, S., Wyatt, B.J. (2010). Binary De Bruijn Partial Words with One Hole. In: KratochvÃl, J., Li, A., Fiala, J., Kolman, P. (eds) Theory and Applications of Models of Computation. TAMC 2010. Lecture Notes in Computer Science, vol 6108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13562-0_13
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DOI: https://doi.org/10.1007/978-3-642-13562-0_13
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