\documentclass[tikz]{standalone}

\usepackage{tikz}

\begin{document}
\usetikzlibrary{automata,positioning}

\iffalse
   $\Sigma = \{A, C, T\}$, $L = \{A^{*}, CTT, CA^{*}\}$
  \fi
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid, auto]
% TODO
	\node[state, initial] (q_0) {$q_{0}$};
	\node[state,right=of q_0] (q_1) {$q_{1}$};
	\node[state,below=of q_0] (q_2) {$q_{2}$};
	\node[state,accepting, right=of q_2] (q_3) {$q_{3}$};

	\path[->] (q_0) edge node {A} (q_1)
	edge node {G} (q_3)
	(q_0) edge node {C} (q_2)
	(q_2) edge node {C} (q_3);
\end{tikzpicture}

\end{document}