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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.03123 |
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| _version_ | 1866914016057622528 |
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| author | Mahalingam, Kalpana Maity, Anuran |
| author_facet | Mahalingam, Kalpana Maity, Anuran |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_03123 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Watson-Crick conjugates of words and languages Mahalingam, Kalpana Maity, Anuran Formal Languages and Automata Theory Combinatorics 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. |
| title | Watson-Crick conjugates of words and languages |
| topic | Formal Languages and Automata Theory Combinatorics |
| url | https://arxiv.org/abs/2208.03123 |