It Is NL-complete to Decide Whether a Hairpin Completion of Regular Languages Is Regular

TL;DR

This paper proves that determining whether the hairpin completion of a regular language remains regular is an NL-complete problem, refining previous complexity bounds and applying to both one-sided and two-sided cases.

Contribution

The authors establish that the regularity decision problem for hairpin completions is NL-complete, improving upon prior polynomial-time results.

Findings

Decidability of regularity is NL-complete

Complexity bound applies to both one-sided and two-sided hairpin completions

Improves previous polynomial-time complexity results

Abstract

The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular language is linear context-free, but not regular, in general. However, for some time it is was open whether the regularity of the hairpin completion of a regular language is is decidable. In 2009 this decidability problem has been solved positively by providing a polynomial time algorithm. In this paper we improve the complexity bound by showing that the decision problem is actually NL-complete. This complexity bound holds for both, the one-sided and the two-sided hairpin completions.