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On the Regularity of Iterated Hairpin Completion of a Single Word

Kari L., Seki S., Kopecki S.

Fundamenta Informaticae

2011

Vol. 110, nr 1-4

201-215

Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand w = xaya, and outputs w' = xayax, where x denotes the Watson- Crick complement of x. In this paper, we focus on the problem of finding conditions under which the iterated hairpin completion of a given word is regular. According to the numbers of words a and a that initiate hairpin completion and how they are scattered, we classify the set of all words w. For some basic classes of words w containing small numbers of occurrences of a and a, we prove that the iterated hairpin completion of w is regular. For other classes with higher numbers of occurrences of a and a, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.