# Automata on genetic structure

Document Type : Research Paper

Authors

1 Department of Mathematics, Dudhnoi College, Dudhnoi-783124, Goalpara, Assam, India.

2 Department of Mathematics, School of Fundamental and Applied Sciences, Assam Don Bosco University, Tepesia-782402, Kamrup, Assam India.

3 Department of Mathematics, University of Gauhati, Guwahati-781014, Assam India.

10.29252/as.2021.2468

Abstract

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 64 codons, obtained from the ordering of the elements of $P$, as the set of states, $A_M$ 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 $M(\Sigma) = (\lbrace f_a : a \in P \rbrace, \circ)$ 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

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