--- a/notes/tex/ue09_notes.tex	Tue Jun 25 00:11:39 2013 +0200
+++ b/notes/tex/ue09_notes.tex	Tue Jun 25 14:27:47 2013 +0200
@@ -19,7 +19,7 @@
             \tikzstyle{rect} = [thick];
             \tikzstyle{caption} = [align=left, anchor=north west];
 
-            \draw[rect, tumblue, fill=tumblue!10] (5.5, 0) rectangle (-5.5, 7) node[caption] {Alle Algorithmen};
+            \draw[rect, tumblue, fill=tumblue!10] (5.5, 0) rectangle (-5.5, 7) node[caption] {Berechenbare Funktionen};
             \draw[rect, dashed, tumred, fill=tumred!10] (4.5, 0.3) rectangle (-4.5, 6) node[caption] {Typ 0 - Rekursiv aufzählbar\\Turingmaschinen, $\lambda$-Kalkül};
             \draw[rect, tumivory, fill=tumivory!10] (3.5, 0.6) rectangle (-3.5, 4.8) node[caption] {Typ 1 - Kontextsensitiv\\CSG};
             \draw[rect, tumorange, fill=tumorange!10] (2.5, 0.9) rectangle (-2.5, 3.6) node[caption] {Typ 2 - Kontextfrei\\PDA, CFG};
@@ -72,36 +72,6 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Programmieren mit TMs}
-    \setbeamercovered{dynamic}
-
-    Sind $f_1$ und $f_2$ Endzustände von $M$, so bezeichnet
-    \begin{center}
-        \begin{tikzpicture}
-            \node (M) at (0, 0) {$M$};
-            \node[above right=0.2cm and 1cm of M] (M1) {$M_1$};
-            \node[below right=0.2cm and 1cm of M] (M2) {$M_2$};
-            \coordinate[right of=M1] (M1s);
-            \coordinate[right of=M2] (M2s);
-
-            \draw[every edge] (-1, 0) -- (M);
-            \draw[every edge] (M) -- node[above left] {$f_1$} (M1);
-            \draw[every edge] (M) -- node[below left] {$f_2$} (M2);
-            \draw[every edge] (M1) -- (M1s);
-            \draw[every edge] (M2) -- (M2s);
-        \end{tikzpicture}
-    \end{center}
-    eine \alert{Fallunterscheidung}.\\
-    \begin{example}[Band=0?]
-    \begin{align*}
-        \delta(q_0, 0) &= (q_0, 0, R) \\
-        \delta(q_0, \square) &= (ja, \square, L) \\
-        \delta(q_0, a) &= (nein, a, N) \qquad \text{für} a \neq 0, \square
-    \end{align*}
-    \end{example}
-\end{frame}
-
-\begin{frame}
     \frametitle{LOOP-Programme}
     \setbeamercovered{dynamic}
 
@@ -173,7 +143,7 @@
     \begin{itemize}
         \item \alert{$add(x, y) = x + y$}
         \item \alert{$mult(x, y) = x \cdot y$}
-        \item $pred(x + 1) = \max \left\{ 0, x \right\}$
+        \item $pred(x) = \max \left\{ 0, x - 1 \right\}$
         \item \alert{$x \dot{-} y = \max \left\{ 0, x - y \right\}$}
         \item $div(x, y) = x \div y$ (Ganzzahldivision)
         \item $mod(x, y) = x \mod y$
@@ -181,7 +151,7 @@
         \item $tower(n) = 2^{2^{2^{\iddots}}}$ mit $tower(4) = 2^{16}$
         \item $sqr(x) = x^2$
         \item $twopow(n) = 2^n$
-        \item $ifthen(n, a, b) = \begin{cases} a & n = 0 \\ b & n \neq 0 \end{cases}$
+        \item $ifthen(n, a, b) = \begin{cases} a & n \neq 0 \\ b & n = 0 \end{cases}$
     \end{itemize}
 \end{frame}
 
@@ -208,6 +178,36 @@
 \end{frame}
 
 \begin{frame}
+    \frametitle{Programmieren mit TMs}
+    \setbeamercovered{dynamic}
+
+    Sind $f_1$ und $f_2$ Endzustände von $M$, so bezeichnet
+    \begin{center}
+        \begin{tikzpicture}
+            \node (M) at (0, 0) {$M$};
+            \node[above right=0.2cm and 1cm of M] (M1) {$M_1$};
+            \node[below right=0.2cm and 1cm of M] (M2) {$M_2$};
+            \coordinate[right of=M1] (M1s);
+            \coordinate[right of=M2] (M2s);
+
+            \draw[every edge] (-1, 0) -- (M);
+            \draw[every edge] (M) -- node[above left] {$f_1$} (M1);
+            \draw[every edge] (M) -- node[below left] {$f_2$} (M2);
+            \draw[every edge] (M1) -- (M1s);
+            \draw[every edge] (M2) -- (M2s);
+        \end{tikzpicture}
+    \end{center}
+    eine \alert{Fallunterscheidung}.\\
+    \begin{example}[Band=0?]
+    \begin{align*}
+        \delta(q_0, 0) &= (q_0, 0, R) \\
+        \delta(q_0, \square) &= (ja, \square, L) \\
+        \delta(q_0, a) &= (nein, a, N) \qquad \text{für} a \neq 0, \square
+    \end{align*}
+    \end{example}
+\end{frame}
+
+\begin{frame}
     \frametitle{WHILE-Programme}
     \setbeamercovered{dynamic}
 

Binary file notes/ue09_notes.pdf has changed