\begin{tikzpicture}[>=stealth, ->, auto, node distance=\dist]
\tikzstyle{every node}=[draw=none]
-\tikzstyle{every state}=[rectangle, rounded corners = 5, minimum size=0.18in, inner sep = 2pt]
+\tikzstyle{every state}=[rectangle, rounded corners = 5, minimum size=0.15in, inner sep = 3pt]
-\tikzset{style1/.style={draw, rectangle, rounded corners = 10, minimum width = \widd, minimum height = 0.3in, xshift = \offs}}
+\tikzset{style1/.style={draw, rectangle, rounded corners = 9, minimum width = \widd, minimum height = 0.25in, xshift = \offs}}
\tikzset{style2/.style={state, accepting, xshift = \offs}}
-\begin{scope}[xshift=4.3in, yshift=1in]
- \node [label={[label distance=0.1in, below left]270:\large{(f)}}] (a) {};
+
+
+
+\begin{scope}[xshift=0in, yshift=0in]
+
+\begin{scope}[xshift=0in, yshift=0.2in]
+ \node [label={[label distance=0.1in, below left]270:\large{(a)}}] (a) {};
\node [label={[label distance=0.1in, below right]270:
- $\begin{aligned}
- &otag \big( (i, j, r) \big) =
- \begin{cases}
- \epsilon &\text{if } i = 0 \\[-0.5em]
- 2i - 1 &\text{if } i \neq 0
- \end{cases}
+$\begin{aligned}
+ &\begin{aligned}
+ f_1 \cdot f_2 &= \big(\Sigma, Q, T, \Delta, x_1, y \big) \\
+ \text{where }
+ &\big(\Sigma, Q_i, T_i, \Delta_i, x_i, y_i\big) = f_i \; \forall i = \overline{1,2}\\
+ &Q = Q_1 \cup \big( Q_2 \setminus \{ x_2 \} \big) \\
+ &T = T_1 \cup T_2 \\
+ &\Delta = \Delta_1
+ \cup \big\{ (z, \alpha, \beta, w) \in \Delta_2 \mid z \neq x_2 \big\} \\[-0.3em]
+ &\hphantom{\Delta = \Delta_1} \cup \big\{ (y_1, \alpha, \beta, w) \mid (x_2, \alpha, \beta, w) \in \Delta_2 \big\}
+ \\
+ &y = \text{if } x_2 = y_2 \text{ then } y_1 \text{ else } y_2
+ \end{aligned}
\\
- &ctag \big( (i, j, r) \big) =
- \begin{cases}
- \epsilon &\text{if } i = 0 \\[-0.5em]
- 2i &\text{if } i \neq 0
- \end{cases}
\\
- &ntag \big( (i, j, r) \big) =
- \begin{cases}
- \epsilon &\text{if } i = 0 \\[-0.5em]
- 1 - 2i &\text{if } i \neq 0
- \end{cases}
- \end{aligned}$}] (a) {};
+ &\begin{aligned}
+ f_1 \mid f_2 &= \big(\Sigma, Q, T, \Delta, x, y_1\big) \\
+ \text{where }
+ &\big(\Sigma, Q_i, T_i, \Delta_i, x_i, y_i\big) = f_i \; \forall i = \overline{1,2}\\
+ &Q = Q_1 \cup \big( Q_2 \setminus \{y_2\} \big) \cup \{x\} \\
+ &T = T_1 \cup T_2 \\
+ &\Delta = \Delta_1
+ \cup \big\{ (z, \alpha, \beta, w) \in \Delta_2 \mid w \neq y_2 \big\} \\[-0.3em]
+ &\hphantom{\Delta = \Delta_1} \cup \big\{ (z, \alpha, \beta, y_1) \mid (z, \alpha, \beta, y_2) \in \Delta_2 \big\} \\[-0.3em]
+ &\hphantom{\Delta = \Delta_1} \cup \big\{ (x, 1, \epsilon, x_1), (x, 2, \epsilon, x_3) \big\} \\[-0.3em]
+ &\hphantom{\Delta = \Delta_1}
+ \text{where } x_3 = \text{if } x_2 = y_2 \text{ then } y_1 \text{ else } x_2
+ \end{aligned}
+ \\
+ \\
+ &\begin{aligned}
+ f^* &= \big(\Sigma, Q, T_1, \Delta, x, y\big) \\
+ \text{where }
+ &\big(\Sigma, Q_1, T_1, \Delta_1, x_1, y_1\big) = f \\
+ &Q = Q_1 \cup \{ y \} \\
+ &\Delta = \Delta_1 \cup
+ \big\{ (y_1, 2, \epsilon, x_1), (y_1, 1, \epsilon, y) \big\}
+ \end{aligned}
+\end{aligned}$
+}] (a) {};
\end{scope}
-\begin{scope}[xshift=0in, yshift=0in]
+\begin{scope}[xshift=0in, yshift=-5.5in]
\def\offs{-0.5in}
\def\widd{1.3in}
- \node[state] (a) {$x$};
- \node[state, accepting, above right of=a, xshift=-0.1in, yshift=-0.1in] (b1) {$x_1$};
- \node[style1, right of = b1] (b) {$F \big( (0, 0, r_1) \big)$};
- \node[style2, right of = b] (b2) {$y_1$};
- \node[state, accepting, below right of=b2, xshift=-0.1in, yshift=0.1in] (d) {$y$};
+ \node[state] (a) {};
+ \node[state, above right of=a, xshift=-0.2in, yshift=-0.2in] (b1) {};
+ \node[style1, right of = b1] (b) {$F ( (0, 0, r) )$};
+ \node[style2, right of = b] (b2) {};
+ \node[state, accepting, below right of=b2, xshift=-0.2in, yshift=0.2in] (d) {};
\path
- (a) edge node {$1 / otag(r) $} (b1)
- (b2) edge node {$1 / ctag(r) $} (d)
+ (a) edge node {$1 / 2i \!-\! 1 $} (b1)
+ (b2) edge node {$1 / 2i $} (d)
;
- \node [label={[label distance=0.1in, below left]270:\large{(a)}}] (a) {};
+ \node [label={[label distance=0.1in, below left]270:\large{(b)}}] (a) {};
\node [label={[label distance=0.1in, below right]270:
$\begin{aligned}
- F \big( r \big) \mid_{r \;=\; (i, \Xund, r_1) \;\wedge\; i \;\neq\; 0} &= (\Sigma, Q, x, \{y\}, \Delta) \\
+ F \big( (i, \Xund, r) \big) \mid_{i \;\neq\; 0} &= \big(\Sigma, Q, T, \Delta, x, y\big) \\
\text{where }
- F \big( (0, 0, r_1) \big) &= (\Sigma, Q_1, x_1, \{y_1\}, \Delta_1) \\
- Q &= Q_1 \cup \{ x, y \}\\
- \Delta &= \Delta_1 \cup
- \big\{ (x, 1, otag(r), x_1), (y_1, 1, ctag(r), y) \big\}
+ &\big(\Sigma, Q_1, T_1, \Delta_1, x_1, y_1\big)= F \big( (0, 0, r) \big) \\
+ &Q = Q_1 \cup \{ x, y \}\\
+ &T = T_1 \cup \big\{ 2i \!-\! 1, 2i \big\} \\
+ &\Delta = \Delta_1 \cup
+ \big\{ (x, 1, 2i \!-\! 1, x_1), (y_1, 1, 2i, y) \big\}
\end{aligned}$
}] (a) {};
\end{scope}
-\begin{scope}[xshift=0in, yshift=-1.4in]
- \node[state] (a) {$x$};
- \node[state, accepting, right of=a] (b) {$y$};
- \path (a) edge node {$1 / \epsilon$} (b);
- \node [label={[label distance=0.1in, below left]270:\large{(b)}}] (a) {};
+\begin{scope}[xshift=0in, yshift=-7.3in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
+
+ \node[state] (a) {};
+ \node[state, right of = a] (a1) {};
+ \node[state, right of = a1] (b1) {};
+ \node[style1, right of = b1] (b) {$ f_2 $};
+ \node[style2, accepting, right of = b] (b2) {};
+ \path
+ (a) edge node {$1 / 1 -\! 2i $} (a1)
+ (a1) edge node {$1 / -\! 2i $} (b1)
+ ;
+ \node [label={[label distance=0.1in, below left]270:\large{(c)}}] (a) {};
+ \node [label={[label distance=0.1in, below right]270:
+ $\begin{aligned}
+ N \big( (0, \Xund, \Xund) \big) &= \big( \Sigma, \{x\}, \emptyset, \emptyset, x, x\big) \\
+ N \big( (i, \Xund, r) \big) &\mid_{i \;\neq\; 0} = f_1 \cdot f_2 \\
+ \text{where }
+ &f_1 = \big( \Sigma, \{x, y, z\}, \big\{ 1 \!-\! 2i, -\! 2i \big\}, \\[-0.3em]
+ &\quad\quad\quad \big\{ (x, 1, 1\!-\!2i, y), (y, 1, -\!2i, z) \big\}, x, z \big) \\
+ &f_2 = \begin{cases}
+ N(r_1) \cdot N(r_2) & \text{if } r = r_1 \cdot r_2 \vee r_1 \mid r_2 \\[-0.3em]
+ N(0, \Xund, \Xund) & \text{if } r \in \{ \epsilon, \alpha \}
+ \end{cases}
+ \end{aligned}$
+ }] (a) {};
+\end{scope}
+
+\end{scope}
+
+
+
+
+\begin{scope}[xshift=4.2in, yshift=0in]
+
+\begin{scope}[xshift=0in, yshift=0in]
+ \node[state, accepting] (a) {};
+ \node [label={[label distance=0.1in, below left]270:\large{(d)}}] (a) {};
\node [label={[label distance=0.1in, below right]270:
- $F \big( (0, 0, \epsilon) \big) = \big(
- \Sigma,
- \{x, y\},
- x,
- \{y\},
- \{ (x, 1, \epsilon, y) \}
- \big)$}] (a) {};
+ $F \big( (0, 0, \epsilon) \big) = \big( \Sigma, \{x\}, \emptyset, \emptyset, x, x \big)
+ $}] (a) {};
\end{scope}
-\begin{scope}[xshift=0in, yshift=-2.2in]
- \node[state] (a) {$x$};
- \node[state, accepting, right of=a] (b) {$y$};
+\begin{scope}[xshift=0in, yshift=-0.7in]
+ \node[state] (a) {};
+ \node[state, accepting, right of=a] (b) {};
\path (a) edge node {$\alpha / \epsilon$} (b);
- \node [label={[label distance=0.1in, below left]270:\large{(c)}}] (a) {};
+ \node [label={[label distance=0.1in, below left]270:\large{(e)}}] (a) {};
\node [label={[label distance=0.1in, below right]270:
- $F \big( (0, 0, \alpha) \big) = \big(
- \Sigma,
- \{x, y\},
- x,
- \{y\},
- \{ (x, \alpha, \epsilon, y) \}
- \big)$
- }] (a) {};
+ $F \big( (0, 0, \epsilon) \big) = \big( \Sigma, \{x, y\}, \emptyset, \{ (x, \alpha, \epsilon, y) \}, x, y \big)
+ $}] (a) {};
\end{scope}
-\begin{scope}[xshift=0in, yshift=-3.1in]
- \def\offs{-0.65in}
- \def\widd{1in}
+\begin{scope}[xshift=0in, yshift=-1.5in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
- \node[state] (a1) {$x_1$};
+ \node[state] (a1) {};
\node[style1, right of = a1] (a) {$F(r_1)$};
- \node[style2, right of = a] (a2) {$y_1$};
+ \node[style2, right of = a] (a2) {};
\node[style1, right of = a2] (b) {$F(r_2)$};
- \node[style2, right of = b] (b2) {$y_2$};
- \node [label={[label distance=0.2in, below left]270:\large{(d)}}] (a) {};
+ \node[style2, right of = b] (b2) {};
+ \node [label={[label distance=0.2in, below left]270:\large{(f)}}] (a) {};
\node [label={[label distance=0.2in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r_1 \cdot r_2) \big) &= (\Sigma, Q, x_1, \{y_2\}, \Delta) \\
- \text{where }
- F(r_i) &= (\Sigma, Q_i, x_i, \{y_i\}, \Delta_i) \; \forall i = \overline{1,2} \\
- Q &= Q_1 \cup Q_2 \setminus \{ x_2 \}\\
- \Delta &= \Delta_1 \cup
- \big\{ (y_1, \alpha, \beta, z) \mid (x_2, \alpha, \beta, z) \in \Delta_2 \big\}
+ F \big( (0, 0, r_1 \cdot r_2) \big) &= F(r_1) \cdot F(r_2)
\end{aligned}$}] (a1) {};
\end{scope}
-\begin{scope}[xshift=0in, yshift=-5.1in]
- \node[state] (a) {$x$};
- \node[state, above right of=a, yshift = -0.4in] (b1) {$x_1$};
- \node[style1, right of = b1] (b) {$F \big( r_1 \big)$};
- \node[style2, right of = b] (b2) {$y_1$};
-
- \node[state, below right of=a, yshift = 0.4in] (c1) {$x_2$};
- \node[style1, right of = c1] (c) {$F \big( r_2 \big)$};
- \node[style2, right of = c] (c2) {$y_2$};
+\begin{scope}[xshift=0in, yshift=-2.8in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
-% \node[draw, rectangle, rounded corners = 6, minimum width = 0.17in, minimum height = 0.67in, right of = b, xshift = \offs, yshift = -0.25in] (ab) {};
- \node[state, accepting] (d) [below right of = b2, yshift = 0.4in] {$y$};
+ \node[state] (a) {};
+ \node[state, above right of = a, yshift = -0.35in] (b1) {};
+ \node[style1, right of = b1] (b) {$F(r_1)$};
+ \node[style2, right of = b] (b2) {};
+ \node[style1, right of = b2, rotate around={-21:(b2)}] (d) {$N(r_2)$};
+
+ \node[state, below right of=a, yshift = 0.35in] (c1) {};
+ \node[style1, right of = c1] (c2) {$N(r_1)$};
+ \node[style2, right of = c2] (c3) {};
+ \node[style1, right of = c3, rotate around={21:(c3)}] (c) {$F(r_2)$};
+ \node[style2, right of = c, rotate around={21:(c)}] (d) {};
\path
(a) edge [bend left] node {$1 / \epsilon$} (b1)
- (a) edge [bend right] node [below left] {$2 / ntag(r_1) $} (c1)
- (b2) edge [bend left] node {$1 / ntag(r_2) $} (d)
- (c2) edge [bend right] node [below right] {$1 / \epsilon$} (d)
+ (a) edge [bend right] node [below left] {$2 / \epsilon $} (c1)
;
-% \path (a) edge [draw=none] node [below=0.6in, midway] {$F \big( (0, 0, (i_1, j_1, r_1) \mid (i_2, j_2, r_2)) \big)$} (d);
- \node [label={[label distance=0.5in, below left]270:\large{(e)}}] (a) {};
+ \node [label={[label distance=0.5in, below left]270:\large{(g)}}] (a) {};
\node [label={[label distance=0.5in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r_1 \mid r_2) \big) &= (\Sigma, Q, x, \{y\}, \Delta) \\
- \text{where }
- F(r_i) &= (\Sigma, Q_i, x_i, \{y_i\}, \Delta_i) \; \forall i = \overline{1,2} \\
- Q &= Q_1 \cup Q_2 \cup \{ x, y \} \\
- \Delta &= \Delta_1 \cup \Delta_2 \cup
- \big\{ (x, 1, \epsilon, x_1), (y_2, 1, \epsilon, y), \\
- & (y_1, 1, ntag(r_2), y), (x, 2, ntag(r_1), x_2)
- \big\}
+ F \big( (0, 0, r_1 \mid r_2) \big) &=
+ \big( F(r_1) \cdot N(r_2) \big) \mid
+ \big( N(r_1) \cdot F(r_2) \big)
\end{aligned}$}] (a) {};
\end{scope}
-\begin{scope}[xshift=4.3in, yshift=-0.7in]
- \def\offs{-0.65in}
- \def\widd{1in}
+\begin{scope}[xshift=0in, yshift=-4in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
\node[state] (a1) {};
\node[style1, right of = a1] (a) {$F(r)$};
\node[style2, right of = a] (a2) {};
- \node[style1, right of = a2, minimum width = 1.8in, xshift = 0.4in] (b) {$F \big( (0, 0, r^{n-1, m-1}) \big)$};
- \node[style2, right of = b, xshift = 0.4in] (b2) {};
- \node [label={[label distance=0.2in, below left]270:\large{(g)}}] (a) {};
+ \node[style1, right of = a2, minimum width = 1.7in, xshift = 0.2in] (b) {$F( (0, 0, r^{n-1, m-1}))$};
+ \node[style2, right of = b, xshift = 0.2in] (b2) {};
+ \node [label={[label distance=0.2in, below left]270:\large{(h)}}] (a) {};
\node [label={[label distance=0.2in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r^{n, m}) \big) \mid_{n \;>\; 1} &= F \big( (0, 0, r \cdot (0, 0, r^{n-1, m-1})) \big)
+ F \big( (0, 0, r^{n, m}) \big) \mid_{n \;>\; 1} &= F \big( (0, 0, r) \big) \cdot F \big( (0, 0, r^{n-1, m-1}) \big)
\end{aligned}$}] (a1) {};
\end{scope}
-\begin{scope}[xshift=4.3in, yshift=-2in]
- \def\offs{-0.25in}
- \def\widd{1.4in}
- \def\dist{0.8in}
-
- \node[state] (a) {$x$};
+\begin{scope}[xshift=0in, yshift=-5.2in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
- \node[state, right of=a] (b1) {$x_1$};
- \node[style1, right of = b1] (b) {$F \big( (0, 0, r^{1,m} \big)$};
- \node[style2, right of = b] (b2) {$y_1$};
+ \node[state] (a) {};
+ \node[state, above right of = a, yshift = -0.35in] (b1) {};
+ \node[style1, right of = b1, rotate around={-21:(b1)}] (d) {$F( (0, 0, r^{1,m}))$};
+ \node[state, below right of=a, yshift = 0.35in] (c1) {};
+ \node[style1, right of = c1, rotate around={21:(c1)}] (c) {$N(r)$};
+ \node[style2, right of = c, rotate around={21:(c)}] (d) {};
\path
- (a) edge node {$1 / \epsilon$} (b1)
+ (a) edge [bend left] node {$1 / \epsilon$} (b1)
+ (a) edge [bend right] node [below left] {$2 / \epsilon $} (c1)
;
- \draw (a) .. controls ($ (a) + (0, 1.5) $) and ($ (b2) + (-1, 1) $) .. node [above] {$2 / ntag(r)$} (b2);
- \node [label={[label distance=0.2in, below left]270:\large{(h)}}] (a) {};
- \node [label={[label distance=0.2in, below right]270:
+ \node [label={[label distance=0.5in, below left]270:\large{(i)}}] (a) {};
+ \node [label={[label distance=0.5in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r^{0, m}) \big) &= (\Sigma, Q, x, \{y_1\}, \Delta) \\
- \text{where }
- F \big( (0, 0, r^{1, m}) \big) &= (\Sigma, Q_1, x_1, \{y_1\}, \Delta_1) \\
- Q &= Q_1 \cup \{ x \} \\
- \Delta &= \Delta_1 \cup
- \big\{ (x, 1, \epsilon, x_1), (x, 2, ntag(r), y_1) \big\}
+ F \big( (0, 0, r^{0, m}) \big) &=
+ \big( F \big( (0, 0, r^{1, m}) \big) \mid
+ \big( N(r) \big) \big)
\end{aligned}$}] (a) {};
\end{scope}
-\begin{scope}[xshift=4.3in, yshift=-3.8in]
- \def\offs{-0.45in}
- \def\widd{1in}
- \def\dist{0.8in}
+\begin{scope}[xshift=0in, yshift=-6.8in]
+ \def\offs{-0.5in}
+ \def\widd{1.3in}
- \node[state] (b1) {$x_1$};
+ \node[state] (b1) {};
\node[style1, right of = b1] (b) {$F(r)$};
- \node[style2, right of = b] (b2) {$y_1$};
+ \node[style2, right of = b] (b2) {};
- \node[state, accepting, right of = b2] (c) {$y$};
+ \node[state, accepting, right of = b2] (c) {};
\path
(b2) edge node {$2 / \epsilon$} (c)
;
\draw (b2) .. controls ($ (b2) + (0.7, 1.5) $) and ($ (b1) + (-0.7, 1.5) $) .. node [above] {$1 / \epsilon$} (b1);
- \node [label={[label distance=0.2in, below left]270:\large{(i)}}] (a) {};
+ \node [label={[label distance=0.2in, below left]270:\large{(j)}}] (a) {};
\node [label={[label distance=0.2in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r^{1, \infty}) \big) &= (\Sigma, Q, x_1, \{y\}, \Delta) \\
- \text{where }
- F(r) &= (\Sigma, Q_1, x_1, \{y_1\}, \Delta_1) \\
- Q &= Q_1 \cup \{ y \} \\
- \Delta &= \Delta_1 \cup
- \big\{ (y_1, 2, \epsilon, x_1), (y_1, 1, \epsilon, y) \big\}
+ F \big( (0, 0, r^{1, \infty}) \big) &= F(r)^*
\end{aligned}$}] (b1) {};
\end{scope}
-\begin{scope}[xshift=4.3in, yshift=-5.8in]
- \def\offs{-0.55in}
- \def\widd{0.8in}
+\begin{scope}[xshift=0in, yshift=-8in]
+ \def\offs{-0.5in}
+ \def\widd{0.9in}
\def\dist{0.8in}
- \node[state] (b1) {$x_1$};
- \node[style1, right of = b1] (b) {$f_1$};
- \node[style2, right of = b] (b2) {$y_1$};
+ \node[state] (b1) {};
+ \node[style1, right of = b1] (b) {$F(r)$};
+ \node[style2, right of = b] (b2) {};
- \node[state, right of = b2] (c1) {$x_2$};
- \node[style1, right of = c1] (c) {$f_2$};
- \node[style2, right of = c] (c2) {$y_2$};
+ \node[state, right of = b2] (c1) {};
+ \node[style1, right of = c1] (c) {$F(r)$};
+ \node[style2, right of = c] (c2) {};
%
\node[state, right of = c2, draw = none] (cd) {\Large{$\dots$}};
%
- \node[state, right of = cd] (d1) {$x_m$};
- \node[style1, right of = d1] (d) {$f_m$};
- \node[style2, right of = d] (d2) {$y_m$};
+ \node[state, right of = cd] (d1) {};
+ \node[style1, right of = d1] (d) {$F(r)$};
+ \node[style2, right of = d] (d2) {};
\path
(c2) edge node {$2 / \epsilon$} (cd)
(cd) edge node {$2 / \epsilon$} (d1)
(b2) edge node {$2 / \epsilon$} (c1)
;
- \draw (b2) .. controls ($ (b2) + (0, 2) $) and ($ (d2) + (-2, 2) $) .. node [very near start] {$1 / \epsilon$} (d2);
- \draw (c2) .. controls ($ (c2) + (0, 1) $) and ($ (d2) + (-2, 1) $) .. node [very near start] {$1 / \epsilon$} (d2);
- \node [label={[label distance=0.2in, below left]270:\large{(j)}}] (a) {};
+ \draw (b2) .. controls ($ (b2) + (0, 2) $) and ($ (d2) + (-1, 2) $) .. node [very near start] {$1 / \epsilon$} (d2);
+ \draw (c2) .. controls ($ (c2) + (0, 1) $) and ($ (d2) + (-1, 1) $) .. node [very near start] {$1 / \epsilon$} (d2);
+ \node [label={[label distance=0.2in, below left]270:\large{(k)}}] (a) {};
\node [label={[label distance=0.2in, below right]270:
$\begin{aligned}
- F \big( (0, 0, r^{1, m}) \big) \mid m \neq \infty &= (\Sigma, Q, x_1, \{y_m\}, \Delta) \\
- \text{where }
- f_i &= F(r) = (\Sigma, Q_i, \{y_i\}, x_i, \Delta_i) \; \forall i = \overline{1, m} \\
- Q &= Q_1 \cup \hdots \cup Q_m \\
- \Delta &= \Delta_1 \cup \hdots \cup \Delta_m
- \cup \big\{ (y_i, 2, \epsilon, x_{i+1}), (y_i, 1, \epsilon, y_m) \big\}_{i=1}^{m-1}
+ &F \big( (0, 0, r^{1, 1}) \big) = F(r) \\
+ &F \big( (0, 0, r^{1, m}) \big) \mid_{1 < m < \infty} =
+ F(r) \cdot
+ \big( F((0,0,\epsilon)) \mid F((0, 0, r^{1, m - 1})) \big)
\end{aligned}$}] (b1) {};
\end{scope}
+\end{scope}
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+ , minimum size=0.15in
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+\begin{scope}[xshift=-0.8in, yshift=-10.5in]
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(x1) edge node [above left] {$1/3$} (z0)
(z0) edge node {$1/\epsilon$} (x15)
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+ (z1) edge node {$1/\!\!-\!\!5$} (z2)
+
(x15) edge node [above left] {$1/5$} (x16)
- (x16) edge [bend left] node [above] {$1/\epsilon$} (x17)
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- (x20) edge [bend right] node [above, near start] {$1/\epsilon$} (x21)
+ (x16) edge [bend left] node [above] {$1/\epsilon$} (x17)
+ (x16) edge [bend right=20] node [above] {$2/\epsilon$} (x21)
+ (x17) edge [bend left] node [above] {$a/\epsilon$} (x21)
(x21) edge node [above right] {$1/6$} (x22)
(x22) edge node [above] {$2/\epsilon$} (y15)
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- (y20) edge [bend right] node [above, near start] {$1/\epsilon$} (y21)
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(y21) edge node [above right] {$1/6$} (y22)
(y22) edge node [above] {$2/\epsilon$} (z15)
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- (z20) edge [bend right] node [above, near start] {$1/\epsilon$} (z21)
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(z21) edge node [above right] {$1/6$} (z22)
(z22) edge node [above right] {$1/4$} (x23)
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(x2) edge [bend left] node [above] {$1/\epsilon$} (x4X)
- (x2) edge [bend right = 20] node [above] {$2/-\!\!9$} (x3Y)
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(x5) edge node [above] {$a/\epsilon$} (x6)
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(x12) edge node [above right] {$1/8$} (x14)
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- \path (x0) edge [draw=none] node [below=0.1in, midway] {\large{(k)} -- TNFA for RE $(a|\epsilon)^{0,3}((a^{0,\infty})|(\epsilon))$} (x24);
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+
+ \path (x0) edge [draw=none] node [below=0.1in, midway] {\large{(l)}} (x24);
\end{scope}
projects / re2c / commitdiff