Text algorithms
Handbook of formal languages, vol. 1
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Partial words and a theorem of Fine and Wilf revisited
Theoretical Computer Science
Theoretical Computer Science
Generalizations of the Periodicity Theorem of Fine and Wilf
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Local periods and binary partial words: an algorithm
Theoretical 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
DNA'04 Proceedings of the 10th international conference on DNA computing
Periodicity properties on partial words
Information and Computation
Combinatorial queries and updates on partial words
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Periodicity algorithms for partial words
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The three-squares lemma for partial words with one hole
Theoretical Computer Science
Hard counting problems for partial words
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
The hardness of counting full words compatible with partial words
Journal of Computer and System Sciences
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Primitive words, or strings over a finite alphabet that cannot be written as a power of another string, play an important role in numerous research areas including formal language theory, coding theory, and combinatorics on words. Testing whether or not a word is primitive can be done in linear time in the length of the word. Indeed, a word is primitive if and only if it is not an inside factor of its square. In this paper, we describe a linear time algorithm to test primitivity on partial words which are strings that may contain a number of ''do not know'' symbols. Our algorithm is based on the combinatorial result that under some condition, a partial word is primitive if and only if it is not compatible with an inside factor of its square. The concept of special, related to commutativity on partial words, is foundational in the design of our algorithm. A World Wide Web server interface at http://www.uncg.edu/mat/primitive/ has been established for automated use of the program.