  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.
