commit 507b35bbc754c5b58d2aab689df18489a0d5511b
parent 5eb7f92f4deb07d587dfdbf3e3a07dba76ee90e7
Author: Georges Dupéron <jahvascriptmaniac+github@free.fr>
Date: Wed, 15 Dec 2010 03:30:10 +0100
Merge branch 'master' of github:jsmaniac/2010-m1s1-complexite
Diffstat:
12 files changed, 3780 insertions(+), 2 deletions(-)
diff --git a/presentation/#.aux b/presentation/#.aux
@@ -0,0 +1 @@
+\relax
diff --git a/presentation/jc.aux b/presentation/jc.aux
@@ -0,0 +1,178 @@
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diff --git a/presentation/jc.tex b/presentation/jc.tex
@@ -0,0 +1,1594 @@
+%Clause Contingente 01 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 02 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+
+ \draw[arr] (1) -- (5) ;
+
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 03 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 04 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 05 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 06 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 07 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 08 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 09 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 10 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 11 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 12 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 13 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 14 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 15 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 16 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 17 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=2] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 18 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[right of=6] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=2] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 19 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[right of=6] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=4] {\textcolor{red}{faux}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=2] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 20 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[right of=5] {\textcolor{green!75!black}{vrai}} ;
+ \node[right of=6] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=4] {\textcolor{red}{faux}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=2] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Contingente 21 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (5) {$x2$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (6) {$x3$} ;
+ \node[lettre] (4) {$\lnot x3$} ;
+ \node[lettre] (7) {$x4$} ;
+ \node[lettre] (2) {$\lnot x4$} ;
+ \node[lettre] (8) {$x1$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[right of=5] {\textcolor{green!75!black}{vrai}} ;
+ \node[right of=3] {\textcolor{red}{faux}} ;
+ \node[right of=6] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=4] {\textcolor{red}{faux}} ;
+ \node[left of=7] {\textcolor{green!75!black}{vrai}} ;
+ \node[left of=2] {\textcolor{red}{faux}} ;
+ \node[left of=8] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, above right of=5] {5} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below right of=6] {6} ;
+ \node[chiffre, below left of=4] {4} ;
+ \node[chiffre, below left of=7] {7} ;
+ \node[chiffre, above left of=2] {2} ;
+ \node[chiffre, above left of=8] {8} ;
+
+ \draw[arr] (1) -- (5) ;
+ \draw[arr] (3) -- (8) ;
+ \draw[arr] (2) -- (6) ;
+ \draw[arr] (4) -- (7) ;
+ \end{tikzpicture}
+ \caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
+ \label{fig:clause-conting}
+\end{figure}
+\end{frame}
+
+%Clause Valide 01 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+%Clause Valide 02 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \path
+ (1) edge[loop above] (1) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 03 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 04 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 05 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 06 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 07 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+
+
+%Clause Valide 08 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+%Clause Valide 09 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 10 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[left of=4] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 11 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[right of=3] {\textcolor{red}{faux}} ;
+ \node[left of=4] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 12 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[right of=2] {\textcolor{green!75!black}{vrai}};
+ \node[right of=3] {\textcolor{red}{faux}} ;
+ \node[left of=4] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+
+%Clause Valide 13 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
+ lettre/.style={
+ on chain,
+ draw,
+ circle,
+ minimum size=1cm
+ },
+ chiffre/.style={
+ node distance = 0.75cm
+ },
+ arr/.style={
+ ->,
+ >=triangle 90
+ }
+ ]
+ \node[lettre] (1) {$\lnot x1$} ;
+ \node[lettre] (2) {$x1$} ;
+ \node[lettre] (3) {$\lnot x2$} ;
+ \node[lettre] (4) {$x2$} ;
+
+ \node[right of=1] {\textcolor{red}{faux}} ;
+ \node[right of=2] {\textcolor{green!75!black}{vrai}};
+ \node[right of=3] {\textcolor{red}{faux}} ;
+ \node[left of=4] {\textcolor{green!75!black}{vrai}} ;
+
+ \node[chiffre, above right of=1] {1} ;
+ \node[chiffre, below right of=2] {2} ;
+ \node[chiffre, below right of=3] {3} ;
+ \node[chiffre, below left of=4] {4} ;
+
+ \path
+ (1) edge[loop above] (1)
+ (2) edge[loop above] (2)
+ (3) edge[loop below] (3)
+ (4) edge[loop above] (4) ;
+ \end{tikzpicture}
+ \caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
+ \label{fig:clause-valide}
+\end{figure}
+\end{frame}
+
+% clause insatisfiable 01 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ node distance=2.5cm,
+ lettre/.style={
+ draw,
+ circle,
+ minimum size=1cm
+ }
+ ]
+ \node[lettre] (nx1) {$\lnot x_1$} ;
+ \node[lettre, below of=nx1] (x1) {$x_1$} ;
+ \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
+ \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
+ \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
+ \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
+
+ \end{tikzpicture}
+ \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
+ \label{fig:clause-insat}
+\end{figure}
+\end{frame}
+
+% clause insatisfiable 02 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ node distance=2.5cm,
+ lettre/.style={
+ draw,
+ circle,
+ minimum size=1cm
+ }
+ ]
+ \node[lettre] (nx1) {$\lnot x_1$} ;
+ \node[lettre, below of=nx1] (x1) {$x_1$} ;
+ \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
+ \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
+ \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
+ \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
+ \draw[->] (nx1l) -- (x1l);
+
+ \end{tikzpicture}
+ \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
+ \label{fig:clause-insat}
+\end{figure}
+\end{frame}
+
+% clause insatisfiable 03 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ node distance=2.5cm,
+ lettre/.style={
+ draw,
+ circle,
+ minimum size=1cm
+ }
+ ]
+ \node[lettre] (nx1) {$\lnot x_1$} ;
+ \node[lettre, below of=nx1] (x1) {$x_1$} ;
+ \node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
+ \node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
+ \node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
+ \node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
+ \draw[->] (x1r) -- (nx1r);
+ \draw[->] (nx1l) -- (x1l);
+ \end{tikzpicture}
+ \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
+ \label{fig:clause-insat}
+\end{figure}
+\end{frame}
+
+% clause insatisfiable 04 - jc
+\begin{frame}
+\begin{figure}[h!]
+ \centering
+ \begin{tikzpicture}[
+ node distance=2.5cm,
+ lettre/.style={
+ draw,
+ circle,
+ minimum size=1cm
+ }
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+ \end{tikzpicture}
+ \caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
+ \label{fig:clause-insat}
+\end{figure}
+\end{frame}
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diff --git a/presentation/presentation.nav b/presentation/presentation.nav
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diff --git a/presentation/presentation.out b/presentation/presentation.out
diff --git a/presentation/presentation.pdf b/presentation/presentation.pdf
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diff --git a/presentation/presentation.snm b/presentation/presentation.snm
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diff --git a/presentation/presentation.tex b/presentation/presentation.tex
@@ -1,6 +1,14 @@
\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[frenchb]{babel}
+\usepackage[utf8]{inputenc}
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+\usepackage{amsmath}
+\usepackage{listings}
+\usepackage{amssymb}
+\usetikzlibrary{chains,positioning,matrix,arrows,decorations,calc}
\usetheme{Warsaw}
\title{FMIN105 \\ Complexité/Calculabilité/Algorithmique}
@@ -22,6 +30,6 @@
Et c'est facile.
\end{frame}
-\end{document}
+\include{jc}
-
+\end{document}
diff --git a/presentation/presentation.toc b/presentation/presentation.toc
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+\select@language {french}
