Watson-Crick conjugates of words and languages

TL;DR

This paper introduces and studies Watson-Crick conjugates (θ-conjugates) of words and languages, extending classical conjugate concepts with DNA complementarity, analyzing their properties, closure, iteration, and decidability issues.

Contribution

It defines θ-conjugates of languages, explores their properties, closure under operations, and investigates decidability problems related to θ-conjugate-free languages.

Findings

Properties of θ-conjugates of words established

Closure properties of language families under θ-conjugation analyzed

Decidability of θ-conjugate-free languages discussed

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.