On the hairpin completion of regular languages

Abstract

The hairpin completion is a natural operation of formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. The hairpin completion of a regular language is linear context-free and we consider the problem to decide whether the hairpin completion remains regular. This problem has been open since the first formal definition of the operation. In this paper we present a positive solution to this problem. Our solution yields more than decidability because we present a polynomial time procedure. The degree of the polynomial is however unexpectedly high, since in our approach it is more than n14. Nevertheless, the polynomial time result is surprising, because even if the hairpin completion H of a regular language L is regular, there can be an exponential gap between the size of a minimal DFA for L and the size of a smallest NFA for H. © 2009 Springer Berlin Heidelberg.