Commit 563b336e authored by Niklas Rieken's avatar Niklas Rieken

finished minimization section, FLM, LMD reviewed, removed fake proofs

parent acbfe22f
\begin{tikzpicture}[sibling distance=15em, every node/.style = {shape=rectangle, rounded corners, draw, align=center}]
\node[top color=cyan!50, bottom color=red!50, middle color=green!50] {$Q = \{q_0, \ldots, q_5\}$}
child { node[top color=cyan!50, bottom color=cyan!50] {$P_1 = F = \{q_2, q_3\}$} }
child { node[top color=green!50, bottom color=red!50] {$P_2 = Q \setminus F = \{q_0, q_1, q_4, q_5\}$}
child { node[top color=green!50, bottom color=green!50] {$P_3 = \{q_0, q_1, q_5\}$} }
child { node[top color=red!50, bottom color=red!50] {$P_4 = \{q_4\}$} }
node[draw=none, yshift=-20pt] {$b, P_1$} };
\end{tikzpicture}
\ No newline at end of file
\begin{tikzpicture}[->, >=stealth', shorten >=1pt, auto, semithick, every state/.style={inner sep=0pt, minimum size=20pt}]
\node[state, initial, initial text=] (0) at (0, 0) {$q_0$};
\node at (1.7, 2.5) {$\mathcal{A}_1$};
\draw[black, rounded corners] (1.5, 2.3) rectangle (4.5, 1.3);
\node[state] (01) at (2, 1.8) {$q_0^1$};
\node[state] (f1) at (4, 1.8) {$q_f^1$};
\node (d1) at (3, 1.8) {$\cdots$};
\node at (1.7, .8) {$\mathcal{A}_2$};
\draw[black, rounded corners] (1.5, .6) rectangle (4.5, -.4);
\node[state] (02) at (2, .1) {$q_0^2$};
\node[state] (f2) at (4, .1) {$q_f^2$};
\node (d2) at (3, .1) {$\cdots$};
\node (dv) at (3, -1.1) {$\vdots$};
\node at (1.7, -1.6) {$\mathcal{A}_n$};
\draw[black, rounded corners] (1.5, -1.8) rectangle (4.5, -2.8);
\node[state] (0n) at (2, -2.3) {$q_0^n$};
\node[state] (fn) at (4, -2.3) {$q_f^n$};
\node (dn) at (3, -2.3) {$\cdots$};
\node[state, accepting] (f) at (6, 0) {$q_f$};
\path (0) edge node {$\varepsilon$} (01)
(0) edge node[below left] {$\varepsilon$} (02)
(0) edge node[below left] {$\varepsilon$} (0n)
(f1) edge node {$1$} (f)
(f2) edge node[below left] {$2$} (f)
(fn) edge node[below right] {$n$} (f);
\end{tikzpicture}
\ No newline at end of file
\begin{tikzpicture}[->, >=stealth', shorten >=1pt, auto, node distance=2.8cm, semithick, every state/.style={inner sep=0pt, minimum size=20pt}]
\node[initial, initial text=, state, top color=green!50, bottom color=green!50] (0) at (0, 0) {$q_0$};
\node[state, top color=green!50, bottom color=green!50] (1) at (2, 0) {$q_1$};
\node[state, accepting, top color=cyan!50, bottom color=cyan!50] (2) at (4, 0) {$q_2$};
\node[state, accepting, top color=cyan!50, bottom color=cyan!50] (3) at (6, 0) {$q_3$};
\node[state, top color=red!50, bottom color=red!50] (4) at (4, -2) {$q_4$};
\node[state, top color=green!50, bottom color=green!50] (5) at (2, -2) {$q_5$};
\path (0) edge[bend left] node {$a$} (1)
(0) edge[bend left=45] node {$b$} (3)
(1) edge[bend left] node {$a$} (0)
(1) edge node {$b$} (2)
(2) edge node {$a$} (3)
(2) edge node {$b$} (4)
(3) edge[loop right] node {$a$} (3)
(3) edge node {$b$} (4)
(4) edge node {$a, b$} (5)
(5) edge node {$a$} (0)
(5) edge node {$b$} (2);
\end{tikzpicture}
\ No newline at end of file
\begin{tikzpicture}[->, >=stealth', shorten >=1pt, auto, node distance=2.8cm, semithick, state/.style={draw, rectangle, rounded corners}]
\node[initial, initial text=, state, top color=green!50, bottom color=green!50] (015) at (0, 0) {$\{q_0, q_1, q_5\}$};
\node[state, accepting, top color=cyan!50, bottom color=cyan!50] (23) at (3, 0) {$\{q_2, q_3\}$};
\node[state, top color=red!50, bottom color=red!50] (4) at (1.5, -2) {$\{q_4\}$};
\node (dummy) at (0, -2.95) {};
\path (015) edge[loop above] node {$a$} (015)
(015) edge node {$b$} (23)
(23) edge[loop above] node {$a$} (23)
(23) edge node {$b$} (4)
(4) edge node {$a, b$} (015);
\end{tikzpicture}
\ No newline at end of file
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