Watson-Crick conjugates of words and languages

In this work, we explore the concept of Watson-Crick conjugates, also known as $θ$-conjugates (where $θ$ is an antimorphic involution), of words and languages. This concept extends the classical idea of conjugates by incorporating the Watson-Crick complementarity of DNA sequences. Our investigation...

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Published inDiscrete Mathematics and Theoretical Computer Science Vol. 27:3; no. Combinatorics; pp. 1 - 32
Main Authors Mahalingam, Kalpana, Maity, Anuran
Format Journal Article
LanguageEnglish
Published Nancy DMTCS 01.10.2025
Discrete Mathematics & Theoretical Computer Science
Subjects
Combinatorics
Conjugates
formal languages and automata theory
Gene sequencing
Investigations
Languages
Mathematics
Word (Linguistics)
Words (language)
India
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ISSN1365-8050
1462-7264
1365-8050
DOI10.46298/dmtcs.13593

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Summary:In this work, we explore the concept of Watson-Crick conjugates, also known as $θ$-conjugates (where $θ$ is an antimorphic involution), of words and languages. This concept extends the classical idea of conjugates by incorporating the Watson-Crick complementarity of DNA sequences. Our investigation initially focuses on the properties of $θ$-conjugates of words. We then define $θ$-conjugates of a language and study closure properties of certain families of languages under the $θ$-conjugate operation. Furthermore, we analyze the iterated $θ$-conjugate of both words and languages. Finally, we discuss the idea of $θ$-conjugate-free languages and examine some decidability problems related to it.
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ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.13593