Closest substring problems for regular languages

Yo Sub Han, Sang Ki Ko, Timothy Ng, Kai Salomaa

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)144-154
Number of pages11
JournalTheoretical Computer Science
Publication statusPublished - 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)


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