automata on genetic structure

In this paper, the authors have represented the genetic structures in terms of automata. with the algebraic structure defined on the genetic code authors defined an au- tomaton on those codons as σ = (cg, p, am , f, g) where p is the set of the four bases a, c, g, u as a set of alphabets or inputs, cg is the set of all 64 codons, obtained from the ordering of the elements of p , as the set of states, am is the set of the 20 amino acids as the set of outputs that produce during the process. f and g are transition function and output function respectively. authors observed that m (σ) = ({fa : a ∈ p }, ◦) defined on the au- tomata σ where fa(q) = f (q, a) = qa, q ∈ cg, a ∈ p is a monoid called the syntactic monoid of σ, with fₐ ◦ fb = fbₐ ∀a, b ∈ p . studying the structure defined in terms of automata it is also observed that the algebraic structure (m (cg), +, ·) forms a near-ring with respect to the two operations ′+′ and ′·′ where m (cg) = {f |f : cg → cg}.