Watson-Crick conjugates of words and languages

Abstract

This paper is a theoretical study of notions in combinatorics of words motivated by information being encoded as DNA strands in DNA computing. We study Watson-Crick conjugates or θ-conjugates, a generalization of the classical notions of conjugates of a word, inspired by biomolecular computing. The Watson-Crick mapping θ is an involution that is also an antimorphism. We study some combinatorial properties of θ-conjugates of a word. We characterize words that have the same set of θ-conjugates. We investigate whether or not the family of certain languages is closed under θ-conjugate operation. We also study the iterated θ-conjugates. We then discuss the concept of θ-conjugate-free language and some decidability problems for θ-conjugate-freeness for different language classes.