Palindromic completion of a word

Motivated by the fact that DNA sequences can be considered as words over the DNA alphabet set {A, C, G, T}, a theoretical study of certain notions in combinatorics on words is done in this paper. The notion of palindromic inverse of a word is generalized to incorporate the notion of an involution function, which is a formalization of the Watson-Crick complementarity and the properties of such words are studied. The set of all left and right palindromic completion of a word is shown to be dense and prolongable but not closed under insertion, deletion and concatenation. Necessary and sufficient conditions are provided so that the set of all left(right)-palindromic completion of a word is closed under concatenation.