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 automaton on those codons as \Sigma = (C_G, P, A_M, F, G) where P is the set of the four bases A, C, G, U as a set of alphabets or inputs, C_G is the set of all ۶۴ codons, obtained from the ordering of the elements of P, as the set of states, A_M is the set of the ۲۰ 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(\Sigma) = (\lbrace f_a : a \in P \rbrace, \circ) defined on the automata \Sigma where f_a(q) = F(q, a) = qa,\ \ q \in C_G, a \in P is a monoid called the syntactic monoid of \Sigma, with f_a \circ f_b = f_{ba} \forall a, b \in P. Studying the structure defined in terms of automata it is also observed that the algebraic structure (M(C_G),\ +,\ \cdot) forms a Near-Ring with respect to the two operations ' + ' and '\cdot ' where M(C_G) = \lbrace f \vert f : C_G \rightarrow C_G \rbrace.

Keywords:

Automata , Transition function , Monoid , Near-ring , Genetic code , Codons