Algebraic properties of DNA operations

Any DNA strand can be identified with a word in the language X* where X={A, C, G, T}. By encoding A as 000, C as 010, G as 101, and T as 111, we treat the DNA operations concatenation, union, reverse, complement, annealing and melting, from the algebraic point of view. The concatenation and union play the roles of multiplication and addition over some algebraic structures, respectively. Then the rest of the operations turn out to be the homomorphisms or anti-homomorphisms of these algebraic structures. Using this technique, we find the relationship among these DNA operations.