Deciding Atomicity of Subword-Closed Languages

Aistis Atminas*, Vadim Lozin

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingConference Proceedingpeer-review

3 Citations (Scopus)


We study languages closed under non-contiguous (scattered) subword containment order. Any subword-closed language L can be uniquely described by its anti-dictionary, i.e. the set of minimal words that do not belong to L. A language L is said to be atomic if it cannot be presented as the union of two subword-closed languages different from L. In this work, we provide a decision procedure which, given a language over a finite alphabet defined by its anti-dictionary, decides whether it is atomic or not.

Original languageEnglish
Title of host publicationDevelopments in Language Theory - 26th International Conference, DLT 2022, Proceedings
EditorsVolker Diekert, Mikhail Volkov
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages9
ISBN (Print)9783031055775
Publication statusPublished - 2022
Event26th International Conference on Developments in Language Theory, DLT 2022 - Tampa, United States
Duration: 9 May 202213 May 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13257 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International Conference on Developments in Language Theory, DLT 2022
Country/TerritoryUnited States


  • Decidability
  • Joint embedding property
  • Subword-closed language


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