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0000000..4be75d9 --- /dev/null +++ b/presentation/jc.log @@ -0,0 +1,34 @@ +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=pdflatex 2010.10.16) 14 DEC 2010 19:12 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**jc.tex +(./jc.tex +LaTeX2e <2009/09/24> +Babel and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, loaded. + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.3 \begin + {figure}[h!] +? x + +Here is how much of TeX's memory you used: + 6 strings out of 495061 + 246 string characters out of 1182620 + 45108 words of memory out of 3000000 + 3282 multiletter control sequences out of 15000+50000 + 3640 words of font info for 14 fonts, out of 3000000 for 9000 + 28 hyphenation exceptions out of 8191 + 7i,0n,5p,36b,20s stack positions out of 5000i,500n,10000p,200000b,50000s +No pages of output. +PDF statistics: + 0 PDF objects out of 1000 (max. 8388607) + 0 named destinations out of 1000 (max. 500000) + 1 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/presentation/jc.tex b/presentation/jc.tex new file mode 100644 index 0000000..2dc13c4 --- /dev/null +++ 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 + } + ] + \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); + \path + (x1) edge[loop below] (x1) + (nx1) edge[loop above] (nx1) ; + \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} diff --git a/presentation/presentation.aux b/presentation/presentation.aux new file mode 100644 index 0000000..01c281b --- /dev/null +++ b/presentation/presentation.aux @@ -0,0 +1,35 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef \newlabel#1#2{\newlabelxx{#1}#2} +\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} 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+\headcommand {\beamer@documentpages {41}} +\headcommand {\def \inserttotalframenumber {41}} diff --git a/presentation/presentation.out b/presentation/presentation.out new file mode 100644 index 0000000..e69de29 diff --git a/presentation/presentation.pdf b/presentation/presentation.pdf new file mode 100644 index 0000000..b15421b Binary files /dev/null and b/presentation/presentation.pdf differ diff --git a/presentation/presentation.snm b/presentation/presentation.snm new file mode 100644 index 0000000..57b8820 --- /dev/null +++ b/presentation/presentation.snm @@ -0,0 +1,38 @@ +\beamer@slide {fig:clause-conting}{4} +\beamer@slide {fig:clause-conting}{5} +\beamer@slide {fig:clause-conting}{6} +\beamer@slide {fig:clause-conting}{7} +\beamer@slide {fig:clause-conting}{8} +\beamer@slide {fig:clause-conting}{9} +\beamer@slide {fig:clause-conting}{10} +\beamer@slide {fig:clause-conting}{11} +\beamer@slide {fig:clause-conting}{12} +\beamer@slide {fig:clause-conting}{13} +\beamer@slide {fig:clause-conting}{14} +\beamer@slide {fig:clause-conting}{15} +\beamer@slide {fig:clause-conting}{16} +\beamer@slide {fig:clause-conting}{17} +\beamer@slide {fig:clause-conting}{18} +\beamer@slide {fig:clause-conting}{19} +\beamer@slide {fig:clause-conting}{20} +\beamer@slide {fig:clause-conting}{21} +\beamer@slide {fig:clause-conting}{22} +\beamer@slide {fig:clause-conting}{23} +\beamer@slide {fig:clause-conting}{24} +\beamer@slide {fig:clause-valide}{25} +\beamer@slide {fig:clause-valide}{26} +\beamer@slide {fig:clause-valide}{27} +\beamer@slide {fig:clause-valide}{28} +\beamer@slide {fig:clause-valide}{29} +\beamer@slide {fig:clause-valide}{30} +\beamer@slide {fig:clause-valide}{31} +\beamer@slide {fig:clause-valide}{32} +\beamer@slide {fig:clause-valide}{33} +\beamer@slide {fig:clause-valide}{34} +\beamer@slide {fig:clause-valide}{35} +\beamer@slide {fig:clause-valide}{36} +\beamer@slide {fig:clause-valide}{37} +\beamer@slide {fig:clause-insat}{38} +\beamer@slide {fig:clause-insat}{39} +\beamer@slide {fig:clause-insat}{40} +\beamer@slide {fig:clause-insat}{41} diff --git a/presentation/presentation.tex b/presentation/presentation.tex index f7fa240..45a266e 100644 --- a/presentation/presentation.tex +++ b/presentation/presentation.tex @@ -1,6 +1,14 @@ \documentclass{beamer} \usepackage[utf8]{inputenc} \usepackage[frenchb]{babel} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[frenchb]{babel} +\usepackage{tikz} +\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 new file mode 100644 index 0000000..462dcbe --- /dev/null +++ b/presentation/presentation.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.07pt} +\select@language {french}