Deciding atomicity of subword-closed languages

We study languages closed under the 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. For a language over a finite alphabet, the anti-dictionary is necessarily f...

Full description

Saved in:
Bibliographic Details
Published inTheoretical computer science Vol. 1003; p. 114595
Main Authors Atminas, A., Lozin, V.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2024
Subjects
Decidability
Joint embedding property
Subword-closed language
Decidability
Joint embedding property
Subword-closed language
Online AccessGet full text

Cover

More Information
Summary:We study languages closed under the 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. For a language over a finite alphabet, the anti-dictionary is necessarily finite. 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. We also develop an algorithmic procedure for decomposing a language, which is not atomic, into finitely many atomic sublanguages.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114595