## Abstract

Hairpin completion, derived from the hairpin formation observed in DNA biochemistry, is an operation applied to strings, particularly useful in DNA computing. Conceptually, a right hairpin completion operation transforms a string S into S · S^{′} where S^{′} is the reverse complement of a prefix of S. Similarly, a left hairpin completion operation transforms a string S into S^{′} · S where S^{′} is the reverse complement of a suffix of S. The hairpin completion distance from S to T is the minimum number of hairpin completion operations needed to transform S into T. Recently Boneh et al. [3] showed an O(n^{2}) time algorithm for finding the hairpin completion distance between two strings of length at most n. In this paper we show that for any ε > 0 there is no O(n^{2−ε})-time algorithm for the hairpin completion distance problem unless the Strong Exponential Time Hypothesis (SETH) is false. Thus, under SETH, the time complexity of the hairpin completion distance problem is quadratic, up to sub-polynomial factors.

Original language | English |
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Title of host publication | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 |

Editors | Shunsuke Inenaga, Simon J. Puglisi |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959773263 |

DOIs | |

State | Published - Jun 2024 |

Event | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 - Fukuoka, Japan Duration: 25 Jun 2024 → 27 Jun 2024 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 296 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 |
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Country/Territory | Japan |

City | Fukuoka |

Period | 25/06/24 → 27/06/24 |

### Bibliographical note

Publisher Copyright:© Itai Boneh, Dvir Fried, Shay Golan, and Matan Kraus.

## Keywords

- Fine-grained complexity
- Hairpin completion
- LCS