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\begin{document}
Aufgabe 3.2.3:\\
\\
Wandeln Sie folgende reguläre Ausdrücke in NEAs mit $\varepsilon$-Übergängen um

\begin{enumerate}
\item
$01^{\ast}$
\item
$(0+1)01$
\item
$00(0+1)^{\ast}$
\end{enumerate}

\begin{enumerate}
\item
NEA mit $\varepsilon$-Übergängen, dessen Sprache die gleiche ist, wie die des regulären Ausdrucks $01^{\ast}$:
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    \thinlines
    \gasset{curvedepth=0,Nw=5,Nh=5}
    \node[Nmarks=i](A1)(0,0){$1$}
    \node(A2)(15,0){$2$}
    \node(A3)(30,0){$3$}
    \node(A4)(45,0){$4$}
    \node(A5)(60,0){$5$}
    \node[Nmarks=r](A6)(74,0){$6$}
    \drawedge(A1,A2){$0$}
    \drawedge(A2,A3){$\varepsilon$}
    \drawedge(A3,A4){$\varepsilon$}
    \drawedge(A4,A5){$1$}
    \drawedge(A5,A6){$\varepsilon$}
    \gasset{curvedepth=5,Nw=5,Nh=5}
    \drawedge(A3,A6){$\varepsilon$}
    \drawedge(A5,A4){$\varepsilon$}
  \end{picture}
  \end{center}
  
\item
NEA mit $\varepsilon$-Übergängen, dessen Sprache die gleiche ist, wie die des regulären Ausdrucks $(0+1)01$
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    \unitlength=4pt
    \begin{picture}(60, 16)(0,-8)
    \gasset{Nw=5,Nh=5,Nmr=2.5,curvedepth=0}
    \thinlines
    \gasset{curvedepth=0,Nw=5,Nh=5}
    \node[Nmarks=i](A1)(0,0){$1$}
    \node(A2)(10,5){$2$}
    \node(A3)(10,-5){$3$}
    \node(A4)(20,5){$4$}
    \node(A5)(20,-5){$5$}
    \node(A6)(30,0){$6$}
    \node(A7)(40,0){$7$}
    \node(A8)(50,0){$8$}
    \node(A9)(60,0){$9$}
    \node[Nmarks=r](A10)(74,0){$F$}
    
    \drawedge(A1,A2){$\varepsilon$}
    \drawedge(A1,A3){$\varepsilon$}
    \drawedge(A2,A4){$0$}
    \drawedge(A3,A5){$1$}
    \drawedge(A4,A6){$\varepsilon$}
    \drawedge(A5,A6){$\varepsilon$}
    \drawedge(A6,A7){$0$}
    \drawedge(A7,A8){$\varepsilon$}
    \drawedge(A8,A9){$1$}
    \drawedge(A9,A10){$\varepsilon$}
  \end{picture}
  \end{center}

\item
NEA mit $\varepsilon$-Übergängen, dessen Sprache die gleiche ist, wie die des regulären Ausdrucks $00(0+1^{\ast})$
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    \begin{picture}(60, 16)(0,-8)
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    \gasset{curvedepth=0,Nw=5,Nh=5}
    \node[Nmarks=i](A1)(0,0){$1$}
    \node(A2)(10,0){$2$}
    \node(A3)(20,0){$3$}
    \node(A4)(30,0){$4$}
    \node(A5)(40,0){$5$}
    \node(A6)(50,5){$6$}
    \node(A7)(50,-5){$7$}
    \node(A8)(60,5){$8$}
    \node(A9)(60,-5){$9$}
    \node(A10)(70,0){$10$}
    \node[Nmarks=r](A11)(80,0){$11$}
    \drawedge(A1,A2){$0$}
    \drawedge(A2,A3){$\varepsilon$}
    \drawedge(A3,A4){$0$}
    \drawedge(A4,A5){$\varepsilon$}
    \drawedge(A5,A6){$\varepsilon$}
    \drawedge(A5,A7){$\varepsilon$}
    \drawedge(A6,A8){$1$}
    \drawedge(A7,A9){$0$}
    \drawedge(A9,A10){$\varepsilon$}
    \drawedge(A8,A10){$\varepsilon$}
    \drawedge(A10,A11){$\varepsilon$}
    \gasset{curvedepth=10,Nw=5,Nh=5}
    \drawedge(A10,A5){$\varepsilon$}
    
    
\end{picture}
\end{center}




\end{enumerate}

\end{document}