On the regularity of iterated hairpin completion of a single word

Details On the regularity of iterated hairpin completion of a single word On the regularity of iterated hairpin completion of a single word

2011-04-13

arxiv.org/abs/1104.2385v1

Computer Science

Formal Languages and Automata Theory

17 pages, 1 figure, submitted to Fundamenta Informaticae

Scientific paper

Hairpin completion is an abstract operation modeling a DNA bio-operation which receives as input a DNA strand $w = x\alpha y \calpha$, and outputs $w' = x \alpha y \bar{\alpha} \bar{x}$, where $\bar{x}$ 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 $\alpha$ and $\calpha$ 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 $\alpha$ and $\calpha$, we prove that the iterated hairpin completion of $w$ is regular. For other classes with higher numbers of occurrences of $\alpha$ and $\calpha$, we prove a necessary and sufficient condition for the iterated hairpin completion of a word in these classes to be regular.

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