\documentclass[11pt]{article}

\usepackage{exscale}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{latexsym}
\usepackage{times,mathptm}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{automata, positioning, arrows, decorations}

\textwidth 6.5truein          
\textheight 9.0truein
\oddsidemargin 0.0in
\topmargin -0.8in

\parindent 0pt          
\parskip 0pt
%\def\baselinestretch{1.1}

\tikzset{
->, % makes the edges directed
%>=stealth’, % makes the arrow heads bold
node distance=3cm, % specifies the minimum distance between two nodes. Change if necessary.
every state/.style={thick, fill=gray!10}, % sets the properties for each ’state’ node
initial text=$ $, % sets the text that appears on the start arrow
}

\begin{document}

\begin{tikzpicture}
\node[state, initial] (q11) {$q_{11}$};
\node[state, right of=q11] (q13) {$q_{13}$};
\node[state, accepting, right of=q13] (q12) {$q_{12}$};
\node[state, accepting, below of=q11] (q21) {$q_{21}$};
\node[state, accepting, right of=q21] (q22) {$q_{22}$};
\node[state, accepting, right of=q22] (q23) {$q_{23}$};

\draw [thick] 
         (q11) edge[loop above, above] node{$0$} (q11)
         (q11) edge[below, above] node{$1$} (q22)
         (q12) edge[bend left, above] node{$0$} (q13)
         (q12) edge[right] node{$1$} (q22)
         (q13) edge[bend left, above] node{$0$} (q12)
         (q13) edge[bend right, left] node{$1$} (q22)
         (q21) edge[left] node{$0$} (q11)
         (q21) edge[below] node{$1$} (q22)
         (q22) edge[loop below, below] node{$1$} (q22)
         (q22) edge[bend right, right] node{$0$} (q13)
         (q23) edge[below] node{$1$} (q22)
         (q23) edge[right] node{$0$} (q12);
\end{tikzpicture}


\begin{tikzpicture}
\node[state, initial] (q11) {$q_{11}$};
\node[state, right of=q11] (q13) {$q_{13}$};
\node[state, accepting, right of=q13] (q12) {$q_{12}$};
\node[state, accepting, below of=q13] (q22) {$q_{22}$};

\draw [thick] 
         (q11) edge[loop above, above] node{$0$} (q11)
         (q11) edge[below, above] node{$1$} (q22)
         (q12) edge[bend left, above] node{$0$} (q13)
         (q12) edge[right] node{$1$} (q22)
         (q13) edge[bend left, above] node{$0$} (q12)
         (q13) edge[bend right, left] node{$1$} (q22)
         (q22) edge[loop below, below] node{$1$} (q22)
         (q22) edge[bend right, right] node{$0$} (q13);
\end{tikzpicture}


\end{document}
