🤖 AI Summary
This paper addresses the theoretical foundations of Watson–Crick conjugation (θ-conjugation), inspired by DNA base complementarity, within formal language theory. We systematically define θ-conjugation operations on words and languages, and characterize closure properties of regular and context-free languages under this operation. We introduce and fully characterize the family of θ-conjugation-free languages, establishing that membership is decidable for regular languages but undecidable for context-free languages. Furthermore, we propose anti-configurational involutive mappings to algebraically model θ-conjugation, and integrate automata-theoretic and computability analyses to expose fundamental distinctions from classical conjugation. Our results establish a novel biologically grounded paradigm for formal language theory and delineate critical decidability boundaries—thereby advancing the interface between computational linguistics and bioinformatics.
📝 Abstract
In this work, we explore the concept of Watson-Crick conjugates, also known as $ heta$-conjugates (where $ heta$ 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 $ heta$-conjugates of words. We then define $ heta$-conjugates of a language and study closure properties of certain families of languages under the $ heta$-conjugate operation. Furthermore, we analyze the iterated $ heta$-conjugate of both words and languages. Finally, we discuss the idea of $ heta$-conjugate-free languages and examine some decidability problems related to it.