 \documentclass[10pt,a4paper,portrait,notitlepage]{report}
\usepackage[utf8]{inputenc}
\usepackage[french]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{ifthen}
\usepackage[top=0.5cm,bottom=0.5cm,left=-2.5cm,right=-2.5cm]{geometry}
\author{Alain Busser\\IREMI 974}
\usepackage{tikz}
\usetikzlibrary{automata,shapes,arrows,shadings}
\tikzset{
v/.style={initial text={\tikz{\node[draw,fill,color=green] {};}},
circle,draw,ultra thick,minimum width=1.4cm},
a/.style={rectangle,draw,ultra thick,minimum width=1.4cm,minimum height=1.4cm},
rouge/.style={->,>=stealth',ultra thick,color=red},
bleu/.style={->,>=stealth',ultra thick,color=blue},
arc/.style={->,>=stealth',ultra thick}
}

\begin{document}



\begin{center}

\begin{tabular}{|c|c|c|}
\hline
$\uparrow$
&
$\downarrow$
&
$+_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[rouge] (a1) to (a0);
\draw[bleu] (a) to (a0);
\draw[rouge] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[bleu] (n) to (a0);
\draw[rouge] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$-_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[bleu] (a1) to (a0);
\draw[rouge] (a) to (a0);
\draw[bleu] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[rouge] (n) to (a0);
\draw[bleu] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$+_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[rouge] (a1) to (a0);
\draw[bleu] (a) to (a0);
\draw[rouge] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[bleu] (n) to (a0);
\draw[rouge] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$-_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[bleu] (a1) to (a0);
\draw[rouge] (a) to (a0);
\draw[bleu] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[rouge] (n) to (a0);
\draw[bleu] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$+_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[rouge] (a1) to (a0);
\draw[bleu] (a) to (a0);
\draw[rouge] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[bleu] (n) to (a0);
\draw[rouge] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$-_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[bleu] (a1) to (a0);
\draw[rouge] (a) to (a0);
\draw[bleu] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[rouge] (n) to (a0);
\draw[bleu] (n) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow$
&
$\downarrow$
&
$+_{1}$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (2,0) {};
\node[v,initial] (a) at (1,1) {}; 
\node[v] (b) at (0,0) {}; 
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (0.5,6) {};
\node[v,accepting] (a0) at (0,5) {};
\node[v] (a1) at (1,5) {};
\draw[rouge] (a1) to (a0);
\draw[bleu] (a) to (a0);
\draw[rouge] (a) to (a1);
\node[v,initial] (n) at (-0.5,6) {};
\draw[bleu] (n) to (a0);
\draw[rouge] (n) to (a);
\end{tikzpicture}
\\
\hline
\end{tabular}

\newpage

\begin{tabular}{|c|c|}
\hline
$\uparrow \uparrow$
&
$\downarrow \downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (1,1) {};
\node[v] (b) at (2,0) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-1,1) {};
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[bleu] (d) to (c);
\draw[rouge] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (1,1) {};
\node[v] (b) at (2,0) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-1,1) {};
\draw[rouge] (a) to (b);
\draw[rouge,bend left=15] (a) to (c);
\draw[bleu,bend right=15] (a) to (c);
\draw[rouge,bend left=15] (b) to (c);
\draw[bleu,bend right=15] (b) to (c);
\draw[rouge] (d) to (c);
\draw[bleu] (d) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow \uparrow$
&
$\downarrow \downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (1,1) {};
\node[v] (b) at (2,0) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-1,1) {};
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[bleu] (d) to (c);
\draw[rouge] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v] (a) at (1,1) {};
\node[v] (b) at (2,0) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-1,1) {};
\draw[rouge] (a) to (b);
\draw[rouge,bend left=15] (a) to (c);
\draw[bleu,bend right=15] (a) to (c);
\draw[rouge,bend left=15] (b) to (c);
\draw[bleu,bend right=15] (b) to (c);
\draw[rouge] (d) to (c);
\draw[bleu] (d) to (a);
\end{tikzpicture}
\\
\hline
$\uparrow \uparrow \uparrow$
&
$\downarrow \downarrow \downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,-1) {};
\node[v] (c) at (2,0) {};
\node[v] (b) at (1,1) {};
\node[v,initial] (a) at (-1,1) {};
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\draw[bleu] (c) to (o);
\draw[rouge] (c) to (d);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,-1) {};
\node[v] (c) at (2,0) {};
\node[v] (b) at (1,1) {};
\node[v,initial] (a) at (-1,1) {};
\draw[rouge,bend left=15] (d) to (o);
\draw[bleu,bend right=15] (d) to (o);
\draw[rouge] (c) to (o);
\draw[bleu] (c) to (d);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (o);
\end{tikzpicture}
\\
\hline
$\uparrow \uparrow \uparrow \uparrow$
&
$\downarrow \downarrow \downarrow \downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (2,0)  {};
\node[v] (d) at (1,-1) {};
\node[v] (e) at (-1,-1) {};
%\node[v] (f) at (-2,0) {};
\node[v,initial] (a) at (-1,1) {};
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\draw[bleu] (b) to (o);
\draw[rouge] (b) to (c);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (o);
\draw[rouge] (c) to (d);
\draw[bleu] (c) to (o);
\draw[bleu] (d) to (e);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (2,0)  {};
\node[v] (d) at (1,-1) {};
\node[v] (e) at (-1,-1) {};
%\node[v] (f) at (-2,0) {};
\node[v,initial] (a) at (-1,1) {};
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\draw[rouge] (b) to (o);
\draw[bleu] (b) to (c);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (o);
\draw[bleu] (c) to (d);
\draw[rouge] (c) to (o);
\draw[rouge] (d) to (e);
\end{tikzpicture}
\\
\hline
$\uparrow \uparrow \uparrow \uparrow \uparrow$
&
$\downarrow \downarrow \downarrow \downarrow \downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (2,0)  {};
\node[v] (d) at (1,-1) {};
\node[v] (e) at (-1,-1) {};
\node[v] (f) at (-2,0) {};
\node[v,initial] (a) at (-1,1) {};
\draw[bleu,bend left=15] (d) to (e);
\draw[rouge,bend right=15] (d) to (e);
\draw[bleu] (b) to (o);
\draw[rouge] (b) to (c);
\draw[bleu,bend left=15] (f) to (o);
\draw[rouge,bend right=15] (f) to (o);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (o);
\draw[rouge] (c) to (d);
\draw[bleu] (c) to (o);
\draw[bleu] (e) to (o);
\draw[rouge] (e) to (f);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (2,0)  {};
\node[v] (d) at (1,-1) {};
\node[v] (e) at (-1,-1) {};
\node[v] (f) at (-2,0) {};
\node[v,initial] (a) at (-1,1) {};
\draw[bleu,bend left=15] (d) to (e);
\draw[rouge,bend right=15] (d) to (e);
\draw[rouge] (b) to (o);
\draw[bleu] (b) to (c);
\draw[bleu,bend left=15] (f) to (o);
\draw[rouge,bend right=15] (f) to (o);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (o);
\draw[bleu] (c) to (d);
\draw[rouge] (c) to (o);
\draw[rouge] (e) to (o);
\draw[bleu] (e) to (f);
\end{tikzpicture}
\\
\hline
\end{tabular}


\newpage

\begin{tabular}{|c|c|}
\hline
$\frac{1}{2}\uparrow$
&
$\frac{1}{2}\downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (a) at (-0.5,1) {};
\node[v] (b) at (0.5,1) {};
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,0) {};
\node[v] (e) at (0,-1) {};
\node[v] (c) at (-1,0) {};
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu] (d) to (o);
\draw[rouge] (d) to (e);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[rouge] (c) to (e);
\draw[rouge] (b) to (d);
\draw[bleu] (b) to (o);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (a) at (-0.5,1) {};
\node[v] (b) at (0.5,1) {};
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,0) {};
\node[v] (e) at (0,-1) {};
\node[v] (c) at (-1,0) {};
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[rouge] (d) to (o);
\draw[bleu] (d) to (e);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[bleu] (c) to (e);
\draw[bleu] (b) to (d);
\draw[rouge] (b) to (o);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (c);
\end{tikzpicture}
\\
\hline
& \\
$\frac{1}{2}\uparrow$
&
$\frac{1}{2}\downarrow$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (a) at (-0.5,1) {};
\node[v] (b) at (0.5,1) {};
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,0) {};
\node[v] (e) at (0,-1) {};
\node[v] (c) at (-1,0) {};
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu] (d) to (o);
\draw[rouge] (d) to (e);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[rouge] (c) to (e);
\draw[rouge] (b) to (d);
\draw[bleu] (b) to (o);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (a) at (-0.5,1) {};
\node[v] (b) at (0.5,1) {};
\node[v,accepting] (o) at (0,0) {};
\node[v] (d) at (1,0) {};
\node[v] (e) at (0,-1) {};
\node[v] (c) at (-1,0) {};
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[rouge] (d) to (o);
\draw[bleu] (d) to (e);
\draw[bleu,bend left=15] (e) to (o);
\draw[rouge,bend right=15] (e) to (o);
\draw[bleu] (c) to (e);
\draw[bleu] (b) to (d);
\draw[rouge] (b) to (o);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (c);
\end{tikzpicture}
\\
\hline
 & \\
$\frac{3}{2}\uparrow$
&
$\frac{3}{2}\downarrow$
\\
\begin{tikzpicture}[scale=1.5]
\node[v] (d) at (-2,2) {};
\node[v] (e) at (0,2) {};
\node[v,accepting] (f) at (2,2) {}; 
\node[v] (b) at (-1,1) {};
\node[v] (c) at (1,1) {};
\node[v] (a) at (-2,0) {};
\node[v,initial] (o) at (2,0) {};
\draw[bleu,bend left=15] (e) to (f);
\draw[rouge,bend right=15] (e) to (f);
\draw[bleu,bend left=15] (c) to (f);
\draw[rouge,bend right=15] (c) to (f);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (d);
\draw[rouge] (o) to (c);
\draw[bleu,bend left] (o) to (a);
\draw[bleu] (b) to (d);
\draw[rouge] (b) to (c);
\draw[rouge] (d) to (e);
\draw[bleu] (e) to (c);
\draw[bleu,bend left] (d) to (f);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=1.5]
\node[v] (d) at (-2,2) {};
\node[v] (e) at (0,2) {};
\node[v,accepting] (f) at (2,2) {}; 
\node[v] (b) at (-1,1) {};
\node[v] (c) at (1,1) {};
\node[v] (a) at (-2,0) {};
\node[v,initial] (o) at (2,0) {};
\draw[bleu,bend left=15] (e) to (f);
\draw[rouge,bend right=15] (e) to (f);
\draw[bleu,bend left=15] (c) to (f);
\draw[rouge,bend right=15] (c) to (f);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (d);
\draw[bleu] (o) to (c);
\draw[rouge,bend left] (o) to (a);
\draw[rouge] (b) to (d);
\draw[bleu] (b) to (c);
\draw[bleu] (d) to (e);
\draw[rouge] (e) to (c);
\draw[rouge,bend left] (d) to (f);
\end{tikzpicture}
\\
\hline
 & \\
$\frac{3}{2}\uparrow$
&
$\frac{3}{2}\downarrow$
\\
\begin{tikzpicture}[scale=1.5]
\node[v] (d) at (-2,2) {};
\node[v] (e) at (0,2) {};
\node[v,accepting] (f) at (2,2) {}; 
\node[v] (b) at (-1,1) {};
\node[v] (c) at (1,1) {};
\node[v] (a) at (-2,0) {};
\node[v,initial] (o) at (2,0) {};
\draw[bleu,bend left=15] (e) to (f);
\draw[rouge,bend right=15] (e) to (f);
\draw[bleu,bend left=15] (c) to (f);
\draw[rouge,bend right=15] (c) to (f);
\draw[bleu] (a) to (b);
\draw[rouge] (a) to (d);
\draw[rouge] (o) to (c);
\draw[bleu,bend left] (o) to (a);
\draw[bleu] (b) to (d);
\draw[rouge] (b) to (c);
\draw[rouge] (d) to (e);
\draw[bleu] (e) to (c);
\draw[bleu,bend left] (d) to (f);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=1.5]
\node[v] (d) at (-2,2) {};
\node[v] (e) at (0,2) {};
\node[v,accepting] (f) at (2,2) {}; 
\node[v] (b) at (-1,1) {};
\node[v] (c) at (1,1) {};
\node[v] (a) at (-2,0) {};
\node[v,initial] (o) at (2,0) {};
\draw[bleu,bend left=15] (e) to (f);
\draw[rouge,bend right=15] (e) to (f);
\draw[bleu,bend left=15] (c) to (f);
\draw[rouge,bend right=15] (c) to (f);
\draw[rouge] (a) to (b);
\draw[bleu] (a) to (d);
\draw[bleu] (o) to (c);
\draw[rouge,bend left] (o) to (a);
\draw[rouge] (b) to (d);
\draw[bleu] (b) to (c);
\draw[bleu] (d) to (e);
\draw[rouge] (e) to (c);
\draw[rouge,bend left] (d) to (f);
\end{tikzpicture}
\\
\hline
\end{tabular}

\newpage

\begin{tabular}{|c|c|}
\hline
& \\
$\uparrow ^2$
&
$+_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-2,0) {};
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[bleu] (d) to (c);
\draw[rouge] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[rouge] (b1) to (b0);
\draw[rouge] (b2) to (b1);
\draw[bleu] (b) to (b0);
\draw[rouge] (b) to (b2);
\draw[bleu] (o) to (b0);
\draw[rouge] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$\downarrow ^2$
&
$-_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-2,0) {};
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[rouge] (d) to (c);
\draw[bleu] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[bleu] (b1) to (b0);
\draw[bleu] (b2) to (b1);
\draw[rouge] (b) to (b0);
\draw[bleu] (b) to (b2);
\draw[rouge] (o) to (b0);
\draw[bleu] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$\uparrow ^3$
&
$\downarrow ^3$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v,initial] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (1,-1) {};
\node[v] (d) at (-1,-1) {};
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[rouge] (b) to (c);
\draw[rouge] (c) to (d);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v,initial] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (1,-1) {};
\node[v] (d) at (-1,-1) {};
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu] (b) to (c);
\draw[bleu] (c) to (d);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\end{tikzpicture}
\\
\hline
& \\
$+_{3}$
&
$+_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,2) {};
\node[v] (c) at (1.5,2) {};
\node[v,accepting] (c0) at (0,1) {};
\node[v] (c1) at (1,1) {};
\node[v] (c2) at (2,1) {};
\node[v] (c3) at (3,1) {};
\draw[rouge] (c1) to (c0);
\draw[rouge] (c2) to (c1);
\draw[rouge] (c3) to (c2);
\draw[bleu] (c) to (c0);
\draw[rouge] (c) to (c3);
\draw[bleu] (o) to (c0);
\draw[rouge] (o) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[rouge] (b1) to (b0);
\draw[rouge] (b2) to (b1);
\draw[bleu] (b) to (b0);
\draw[rouge] (b) to (b2);
\draw[bleu] (o) to (b0);
\draw[rouge] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$-_{3}$
&
$-_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,2) {};
\node[v] (c) at (1.5,2) {};
\node[v,accepting] (c0) at (0,1) {};
\node[v] (c1) at (1,1) {};
\node[v] (c2) at (2,1) {};
\node[v] (c3) at (3,1) {};
\draw[bleu] (c1) to (c0);
\draw[bleu] (c2) to (c1);
\draw[bleu] (c3) to (c2);
\draw[rouge] (c) to (c0);
\draw[bleu] (c) to (c3);
\draw[rouge] (o) to (c0);
\draw[bleu] (o) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[bleu] (b1) to (b0);
\draw[bleu] (b2) to (b1);
\draw[rouge] (b) to (b0);
\draw[bleu] (b) to (b2);
\draw[rouge] (o) to (b0);
\draw[bleu] (o) to (b);
\end{tikzpicture}
\\
\hline
\end{tabular}




\newpage

\begin{tabular}{|c|c|}
\hline
& \\
$\uparrow ^2$
&
$+_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-2,0) {};
\draw[rouge] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[bleu] (d) to (c);
\draw[rouge] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[rouge] (b1) to (b0);
\draw[rouge] (b2) to (b1);
\draw[bleu] (b) to (b0);
\draw[rouge] (b) to (b2);
\draw[bleu] (o) to (b0);
\draw[rouge] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$\downarrow ^2$
&
$-_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v,accepting] (c) at (0,0) {};
\node[v,initial] (d) at (-2,0) {};
\draw[bleu] (a) to (b);
\draw[bleu,bend left=15] (a) to (c);
\draw[rouge,bend right=15] (a) to (c);
\draw[bleu,bend left=15] (b) to (c);
\draw[rouge,bend right=15] (b) to (c);
\draw[rouge] (d) to (c);
\draw[bleu] (d) to (a);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[bleu] (b1) to (b0);
\draw[bleu] (b2) to (b1);
\draw[rouge] (b) to (b0);
\draw[bleu] (b) to (b2);
\draw[rouge] (o) to (b0);
\draw[bleu] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$\uparrow ^3$
&
$\downarrow ^3$
\\
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v,initial] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (1,-1) {};
\node[v] (d) at (-1,-1) {};
\draw[bleu] (a) to (o);
\draw[rouge] (a) to (b);
\draw[rouge] (b) to (c);
\draw[rouge] (c) to (d);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,accepting] (o) at (0,0) {};
\node[v,initial] (a) at (-1,1) {};
\node[v] (b) at (1,1) {};
\node[v] (c) at (1,-1) {};
\node[v] (d) at (-1,-1) {};
\draw[rouge] (a) to (o);
\draw[bleu] (a) to (b);
\draw[bleu] (b) to (c);
\draw[bleu] (c) to (d);
\draw[bleu,bend left=15] (b) to (o);
\draw[rouge,bend right=15] (b) to (o);
\draw[bleu,bend left=15] (c) to (o);
\draw[rouge,bend right=15] (c) to (o);
\draw[bleu,bend left=15] (d) to (o);
\draw[rouge,bend right=15] (d) to (o);
\end{tikzpicture}
\\
\hline
& \\
$+_{3}$
&
$+_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,2) {};
\node[v] (c) at (1.5,2) {};
\node[v,accepting] (c0) at (0,1) {};
\node[v] (c1) at (1,1) {};
\node[v] (c2) at (2,1) {};
\node[v] (c3) at (3,1) {};
\draw[rouge] (c1) to (c0);
\draw[rouge] (c2) to (c1);
\draw[rouge] (c3) to (c2);
\draw[bleu] (c) to (c0);
\draw[rouge] (c) to (c3);
\draw[bleu] (o) to (c0);
\draw[rouge] (o) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[rouge] (b1) to (b0);
\draw[rouge] (b2) to (b1);
\draw[bleu] (b) to (b0);
\draw[rouge] (b) to (b2);
\draw[bleu] (o) to (b0);
\draw[rouge] (o) to (b);
\end{tikzpicture}
\\
\hline
& \\
$-_{3}$
&
$-_{2}$
\\
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,2) {};
\node[v] (c) at (1.5,2) {};
\node[v,accepting] (c0) at (0,1) {};
\node[v] (c1) at (1,1) {};
\node[v] (c2) at (2,1) {};
\node[v] (c3) at (3,1) {};
\draw[bleu] (c1) to (c0);
\draw[bleu] (c2) to (c1);
\draw[bleu] (c3) to (c2);
\draw[rouge] (c) to (c0);
\draw[bleu] (c) to (c3);
\draw[rouge] (o) to (c0);
\draw[bleu] (o) to (c);
\end{tikzpicture}
&
\begin{tikzpicture}[scale=2]
\node[v,initial] (o) at (0,4) {};
\node[v] (b) at (1,4) {};
\node[v,accepting] (b0) at (0,3) {};
\node[v] (b1) at (1,3) {};
\node[v] (b2) at (2,3) {};
\draw[bleu] (b1) to (b0);
\draw[bleu] (b2) to (b1);
\draw[rouge] (b) to (b0);
\draw[bleu] (b) to (b2);
\draw[rouge] (o) to (b0);
\draw[bleu] (o) to (b);
\end{tikzpicture}
\\
\hline
\end{tabular}









\end{center}

 
\end{document}


