@article { author = {Dutta, Mridul and Kalita, Sanjoy and Saikia, Helen}, title = {Automata on genetic structure}, journal = {Algebraic Structures and Their Applications}, volume = {9}, number = {1}, pages = {109-119}, year = {2022}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/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 = {Automata,Transition function,Monoid,Near-ring,Genetic code,Codons}, url = {https://as.yazd.ac.ir/article_2468.html}, eprint = {https://as.yazd.ac.ir/article_2468_3b6869b39d2878ec80277a08669967a3.pdf} }