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Watson-Crick conjugates of words and languages

Published 5 Aug 2022 in cs.FL and math.CO | (2208.03123v3)

Abstract: In this work, we explore the concept of Watson-Crick conjugates, also known as $\theta$-conjugates (where $\theta$ 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 $\theta$-conjugates of words. We then define $\theta$-conjugates of a language and study closure properties of certain families of languages under the $\theta$-conjugate operation. Furthermore, we analyze the iterated $\theta$-conjugate of both words and languages. Finally, we discuss the idea of $\theta$-conjugate-free languages and examine some decidability problems related to it.

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