% g.tex
% Patrick Simianer <p@simianer.de>
% 2010-05-24
\documentclass{scrartcl}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
\usepackage{lmodern}

\usepackage{tikz}
\usetikzlibrary{arrows,automata}


\begin{document}


$a*$\\

\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] (A)              		  {$\{2, 3\}$};
  \node[state,accepting]         (B) [below of=A] {$\{0, 1, 3\}$};

  \path[->] (A) edge              node {$\ \ \ \ a$} (B)
			(B) edge [loop below] node {$a$} ();
\end{tikzpicture}

\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial]   (s2)              		 {$2$};
  \node[state,accepting] (s3) [right of=s2]      {$3$};
  \node[state] (s0) [below left of=s2] {$0$};
  \node[state] (s1) [below left of=s3] {$1$};
  

\path[->] (s2) edge              node {$\epsilon$} (s3)
		  (s2) edge              node {$a$} (s0)
		(s0) edge     [bend right]         node {$\epsilon$} (s1)
		(s1) edge     [bend right]         node {$a$} (s0)
		(s1) edge              node {$\epsilon$} (s3);

\end{tikzpicture}



\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial]   (s2)              		 {$2$};
  \node[state] 			 (s0) [right of=s2]      {$0$};
  \node[state] 			 (s1) [right of=s0] 	 {$1$};
  \node[state,accepting] (s3) [right of=s1]      {$3$};
  

\path[->] (s2) edge    [bend right]          node {$\epsilon$} (s3)
		  (s2) edge              			 node {$\epsilon$} (s0)
		  (s0) edge              			 node {$a$} (s1)
		  (s1) edge        [bend right]      node {$\epsilon$} (s0)
		  (s1) edge              			 node {$\epsilon$} (s3);
\end{tikzpicture}


$(a|b)*$\\

\begin{tikzpicture}[shorten >=1pt,node distance=2cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (s6)              				  	{$6$};
  \node[state]	 				 (s4)      [right of=s6]       		{$4$};
  \node[state]	 				 (s0)      [above right of=s4]      {$0$};
  \node[state]	 				 (s2)      [below right of=s4]      {$2$};
  \node[state]	 				 (s1)      [right of=s0]        	{$1$};
  \node[state]	 				 (s3)      [right of=s2]     		{$3$};
  \node[state]	 				 (s5)      [below right of=s1]      {$5$};
  \node[state,accepting] 		 (s7)      [right of=s5]            {$7$};

\path[->] (s6) edge    node {$\epsilon$} (s4)
		  (s4) edge    node {$\epsilon$} (s0)
	      (s4) edge    node {$\epsilon$} (s2)
		  (s0) edge    node {$a$} (s1)
		  (s2) edge    node {$b$} (s3)
		  (s1) edge    node {$\epsilon$} (s5)
		  (s3) edge    node {$\epsilon$} (s5)
		  (s5) edge    node {$\epsilon$} (s4)
		(s5) edge    node {$\epsilon$} (s7)
		(s6) edge [bend right]   node {$\epsilon$} (s7);
\end{tikzpicture}


\begin{tikzpicture}[shorten >=1pt,node distance=4cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial]   (A)              		 {$\{6,7,4,0,2\}$};
  \node[state] 			 (B) [below left  of=A]  {$\{1,5,7,4,0,2\}$};
  \node[state,accepting] (C) [below right of=A]  {$\{3,5,7,4,0,2\}$};
  

\path[->] (A) edge              node {$a$} (B)
 		  (A) edge              node {$b$} (C)
		  (B) edge    [loop below]          node {$a$} (B)
		  (C) edge    [loop below]          node {$b$} (C)
		(B) edge    [bend right]          node {$b$} (C)
		(C) edge    [bend right]          node {$a$} (B);
\end{tikzpicture}

$a*b|b*a$\\

\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (s12)              {$12$};

  \node[state]         (s2)  [above right of=s12]  	{$2$};
  \node[state]         (s3)  [right of=s2]  			{$3$};
  \node[state]         (s0)  [above of=s2]  			{$0$};
  \node[state]         (s1)  [above of=s3]  			{$1$};
  \node[state]         (s4)  [right of=s3]  			{$4$};
  \node[state]         (s5)  [right of=s4]  			{$5$};

  \node[state]         (s8) [below right of=s12]   	{$8$};
  \node[state]         (s6) [below of=s8]   			{$6$};
  \node[state]         (s7) [right of=s6]   			{$7$};
  \node[state]         (s9) [right of=s8]   			{$9$};
  \node[state]         (s10) [right of=s9]   			{$10$};
  \node[state]         (s11) [right of=s10]   		{$11$};

  \node[state,accepting]         (s13) [below right of=s5]   	{$13$};

\path[->]
(s12) edge              node {$\epsilon$} (s2)
(s2) edge              node {$\epsilon$} (s0)
(s0) edge    [bend right]          node {$a$} (s1)
(s1) edge    [bend right]          node {$\epsilon$} (s0)
(s1) edge              node {$\epsilon$} (s3)
(s2) edge              node {$\epsilon$} (s3)
(s3) edge              node {$\epsilon$} (s4)
(s4) edge              node {$b$} (s5)
(s5) edge              node {$\epsilon$} (s13)

(s12) edge              node {$\epsilon$} (s8)
(s8) edge              node {$\epsilon$} (s6)
(s6) edge  [bend right]            node {$b$} (s7)
(s7) edge  [bend right]            node {$\epsilon$} (s6)
(s8) edge              node {$\epsilon$} (s9)
(s7) edge              node {$\epsilon$} (s9)
(s9) edge              node {$\epsilon$} (s10)
(s10) edge              node {$a$} (s11)
(s11) edge              node {$\epsilon$} (s13);
\end{tikzpicture}


\begin{tikzpicture}[shorten >=1pt,node distance=5cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (A)              				{$\{12,2,0,3,4,8,6,9,10\}$};

  \node[state,accepting] 		 (B)   [above right of=A]      {$\{1, 3, 4, 0, 11, 13\}$};
  \node[state] 		 (C)   [right of=B]           {$\{1, 3, 4, 0\}$};
  \node[state,accepting] 		 (D)   [right of=C]           {$\{5, 13\}$};

  \node[state,accepting] 		 (E)   [below right of=A]           {$\{7,9,10,6,5,13\}$};
  \node[state,accepting] 		 (F)   [right of=E]           {$\{7,9,10,6\}$};
  \node[state,accepting] 		 (G)   [right of=F]           {$\{11,13\}$};


\path[->] (A) edge node {$a$} (B)
		  (B) edge [bend left] node {$b$} (D)
		  (B) edge node {$a$} (C)
          (C) edge [loop below] node {$a$} (C)
		  (C) edge node {$b$} (D)
		
		(A) edge node {$b$} (E)
		(E) edge [bend right] node {$a$} (G)
		
				  (E) edge node {$b$} (F)
		          (F) edge [loop above] node {$b$} (F)
				  (F) edge node {$a$} (G);
\end{tikzpicture}



\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] (A)              		  {};
  \node[state,accepting]         (B) [right of=A] {};

  \path[->] (A) edge              node {$a$} (B);
\end{tikzpicture}\\

\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] (A)              		  {};
  \node[state,accepting]         (B) [right of=A] {};

  \path[->] (A) edge              node {$\epsilon$} (B);
\end{tikzpicture}

$ab$\\
\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (A)              		  {};
  \node[state,accepting]         (B) [right of=A] 		  {};
  \node[state]         (C) [right of=B] 		  {};
  \node[state,accepting]         (D) [right of=C] 		  {};

  \path[->]
(A) edge              node {$a$} (B)
(B) edge              node {$\epsilon$} (C)
(C) edge              node {$b$} (D);
\end{tikzpicture}



$(a|b)$\\
\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (A)              		  {};
  \node[state]         (B) [above right of=A] 		  {};
  \node[state]         (C) [below right of=A] 		  {};
  \node[state,accepting]         (D) [right of=B] 		  {};
  \node[state,accepting]         (E) [right of=C] 		  {};
  \node[state,accepting]         (F) [above right of=E] 		  {};

\path[->]  (A) edge node {$\epsilon$} (B)
(A) edge node {$\epsilon$} (C)

(B) edge node {$a$} (D)
(C) edge node {$b$} (E)


(D) edge node {$\epsilon$} (F)
(E) edge node {$\epsilon$} (F)
;
\end{tikzpicture}




$a*$\\
\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick]
  \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20]

  \node[state,initial] 			 (A)              		  {};
  \node[state]         (B) [right of=A] 		  {};
  \node[state,accepting]         (C) [right of=B] 		  {};
  \node[state,accepting]         (D) [right of=C] 		  {};

  \path[->]
(A) edge              node {$\epsilon$} (B)
(B) edge              node {$a$} (C)
(C) edge  [bend right]            node {$\epsilon$} (B)

(C) edge              node {$\epsilon$} (D)
(A) edge       [bend right]       node {$\epsilon$} (D);

\end{tikzpicture}


\end{document}