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@ -130,6 +130,66 @@
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\( \sigma(Z_2,\Box) = (Z_a, \Box, R) \)\\
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\( \sigma(Z_2,\Box) = (Z_a, \Box, R) \)\\
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\( \sigma(Z_1,\Box) = (Z_a, 1, N) \)
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\( \sigma(Z_1,\Box) = (Z_a, 1, N) \)
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Als Diagramm
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% TODO
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\( L = \{ 0^{2^n} \mid n \ge 0 \} \)\\
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\( 0, 00, 0^4, 0^8, …\)
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\begin{tabular}{c|c|c|c|c|c}
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\hline
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& 0 & 0 & 0 & 0 & \\
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\hline
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\end{tabular}
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\begin{enumerate}
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\item Vorschlag: Zähle\\
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\begin{tabular}{c|c|c|c|c|c}
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\hline
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& \( \not0\) & 0 & … 0 & \( \Box \) & 0\\
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\hline
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\end{tabular}
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\item Vorschlag:\\
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\begin{enumerate}
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\item streiche jede 2. Null, teste dabei, ob Anzahl gerade
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\item iteriere Schritt 1\\
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bis nur noch eine Null bleibt.\\
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% TODO: Diagramm
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\( 0000 \to 0x0x \to 0xxx \)
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\end{enumerate}
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\end{enumerate}
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\subsection{Erweiterungen}
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\subsubsection{Mehrband-Turingmaschine}
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Turingmaschine mit fester Anzahl k von Bändern. Davon eins ausgezeichnet für die Eingabe.\\
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\( \delta: Z \times \Gamma^k \to Z \times \Gamma^k \times \{ L,N,R \}^k \)
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Bsp.:\\
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\( \delta(Z,a,b) = \delta(Z', c,d,L,R) \)
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Bsp.: \( L = \left\{ w \# w \mid w \in \{0,1\}^k \right\} \)\\
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\( 100\#100 \to x00\#x00 …\)
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\underline{2-Band-Turingmaschine}\\
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kopiert w auf 2. Band\\
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\spa \( \delta(Z_0, a, \Box) = (Z_0,a,a,R,R) \) für \( a \in \{1,0\}\)\\
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\spa \( \delta(Z_0, \#,\Box) = (Z_1, \#,\Box, N,L) \)\\
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\spa \( \delta(Z_1, \#,\Box) = (Z_1, \#,a, N,L)\)\\
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\spa \( \delta(Z_1, \#,\Box) = (Z_2, \#,\Box,R,R) \)\\
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\spa \( \delta(Z_2, a,a) = (Z_2,a,a,R,R) \)\\
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\spa \( \delta(Z_2, \Box,\Box) = (Z_a, \Box,\Box,N,N) \)
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Alles was fehlt geht nach \( Z_V \)
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\subsubsection{Nichtdeterministische Turingmaschine (NTM)}
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Definiert wie Turingmaschine, mit:\\
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\spa \( \delta: Z\times \Gamma \to \mathcal{P}(Z \times \Gamma \times \{ L,N,R \}) \)\\
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z.\,B. \( \delta(Z,a) = \{ (Z_1,b,L) , (Z_2,c,N) \} \)
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M akzeptiert x, falls es eine akzeptierende Rechnung gibt.
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\end{document}
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\end{document}
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