Handbook of formal languages, vol. 1
Inventories of unavoidable languages and the word-extension conjecture
Theoretical Computer Science
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Efficient string matching: an aid to bibliographic search
Communications of the ACM
An Algorithm for Approximate Tandem Repeats
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Finding approximate repetitions under Hamming distance
Theoretical Computer Science - Logic and complexity in computer science
Partial words and the critical factorization theorem
Journal of Combinatorial Theory Series A
Codes, orderings, and partial words
Theoretical Computer Science
Discrete Applied Mathematics
Note: Testing avoidability on sets of partial words is hard
Theoretical Computer Science
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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.