## Abstract

The CLOSEST SUBSTRING problem asks whether there exists a consensus string w of given length ℓ such that each string in a set of strings L has a substring whose edit distance is at most r (called the radius) from w. The CLOSEST SUBSTRING problem has been studied for finite sets of strings and is known to be NP-hard. We show that the CLOSEST SUBSTRING problem for regular languages represented by nondeterministic finite automata (NFA) is PSPACE-complete. The problem remains PSPACE-hard even when the input is a deterministic finite automaton and the length ℓ and radius r are given in unary. Also we show that the CLOSEST SUBSTRING problem for acyclic NFAs lies in the second level of the polynomial-time hierarchy and is both NP-hard and coNP-hard.

Original language | English |
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Pages (from-to) | 144-154 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 862 |

DOIs | |

Publication status | Published - 2021 Mar 16 |

### Bibliographical note

Funding Information:Han was supported by the Institute for Information & Communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (2018-0-00276).Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A4A307994711).Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Publisher Copyright:

© 2020 Elsevier B.V.

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)