diff --git a/docs/.gitignore b/docs/.gitignore
old mode 100644
new mode 100755
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/conclusion/index.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/conclusion/index.tex
new file mode 100644
index 0000000000000000000000000000000000000000..82be84b945f6d718986aae9a94470433c13d3cb6
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/conclusion/index.tex
@@ -0,0 +1,15 @@
+\begin{frame}
+ \frametitle{Conclusion}
+
+ \begin{block}{What's next ?}
+ \begin{itemize}
+ \item Study and formalize some "in-prod" algoritms using weak consistency in byzantin contexts.
+ \item Continue the colaboration with Parsec:
+ \begin{itemize}
+ \item formalize a list of properties
+ \item provide a proof of concept of a colaborative editor
+ \end{itemize}
+
+ \end{itemize}
+ \end{block}
+\end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/byzantin.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/byzantin.tex
new file mode 100644
index 0000000000000000000000000000000000000000..1288908fc529c142a25c1375bd396ac7da1ef05c
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/byzantin.tex
@@ -0,0 +1,14 @@
+\begin{frame}
+ \frametitle{The Byzantin context associate to the weak consistency}
+
+ \begin{block}{Some questions about:}
+ \begin{itemize}
+ \item is the weak consistency introduce new possibility of malicious behaviours.
+ \item is the weak consistency reduce by design the field of milicious behaviours.
+ \end{itemize}
+ \end{block}
+
+ The state of the art is poor about these questions and few formalized algoritms are avaible.
+
+
+\end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/faible.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/faible.tex
new file mode 100644
index 0000000000000000000000000000000000000000..42577cfce6546c0d7c97e0ff258e8f6c190daea1
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/faible.tex
@@ -0,0 +1,122 @@
+\begin{frame}
+ \frametitle{The models of consistency}
+
+ \begin{columns}
+ \column{0.6\textwidth}
+ \footnote{Perrin, \emph{Concurrence et cohérence dans les systèmes répartis}, 2017}
+ \resizebox{\columnwidth}{!}{
+ \includegraphics{images/carte_criteres.png}
+ }
+
+ \column{0.4\columnwidth}
+ \begin{block}{Les classes de cohérences}
+ 2 big family :
+ \begin{itemize}
+ \item Strong Consistency
+ \item Weak Consistency :
+ \begin{itemize}
+ \item Eventual Consistency (EC)
+ \item State Locality (SL)
+ \item Validity (V)
+ \end{itemize}
+ \end{itemize}
+ \end{block}
+ \end{columns}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Eventual Consistency (EC)}
+
+ \begin{block}{Definition}
+ There exist a set of confinite operations where each one must be justify with the same state.
+ \end{block}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=green!50!black]
+ \input{schemas/convergence_hc_1}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ $E' = \{r/(1,2)^\omega, r/(1,2)^\omega\}$ \newline
+ $\delta = ((1,2), \emptyset)$ is a valid state justifying $E'$.
+ \end{columns}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=red!50!black]
+ \input{schemas/convergence_hc_2}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ $E' = \{r/(1,2)^\omega, r/(2,1)^\omega\}$. \newline
+ There exist no state able to justify $E'$ because the two infinite read are not consistent.
+ \end{columns}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{State Locality}
+
+ \begin{block}{Definition}
+ For all $p$, there exist one linearization who include all the read operations of $p$. According to the local order of these reads. \\
+ \end{block}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=green!50!black]
+ \input{schemas/localiteetat_hc_1}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ \begin{math}
+ \begin{array}{l}
+ \textcolor{blue}{C_{p_0} = \{r/(0,0), r/(0,2)^\omega, w(2)\}}, \\
+ \textcolor{red}{C_{p_1} = \{r/(0,0), r/(0,1)^\omega, w(1)\}}, \\
+ \textcolor{blue}{r/(0,0) \bullet w(2) \bullet r/(0,2)^\omega} \\
+ \textcolor{red}{r/(0,0) \bullet w(1) \bullet r/(0,1)^\omega} \\
+ \end{array}
+ \end{math}
+ \end{columns}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=red!50!black]
+ \input{schemas/localiteetat_hc_2}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ $E'_{p_0} = \{r/(0,0), r/(2,1)^\omega\},$ \newline
+ $r/(0,0) \bullet w(2) \bullet w(1) \bullet r/(2,1)^\omega$ \newline
+ $E'_{p_1} = \{r/(0,1), r/(2,1)^\omega\}$. \newline
+ There exist no linearization of $p_1$ satisfying the definition of state locality
+ \end{columns}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Validity (V)}
+
+ \begin{block}{Definition}
+ There exist a cofinite set of operations such as for each of them must be justified by a linearization of all the write operation.
+ \end{block}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=green!50!black]
+ \input{schemas/validite_hc_1}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ \begin{math}
+ \begin{array}{ll}
+ E' = & \{r/(2,1)^\omega, r/(1,2)^\omega\} \\
+ & w(2) \bullet w(1) \bullet \textcolor{red}{r/(2,1)^\omega} \\
+ & w(1) \bullet w(2) \bullet \textcolor{red}{r/(1,2)^\omega} \\
+ \end{array}
+ \end{math}
+ \end{columns}
+
+ \begin{columns}
+ \column{0.4\columnwidth}
+ \begin{tcolorbox}[colframe=red!50!black]
+ \input{schemas/validite_hc_2}
+ \end{tcolorbox}
+ \column{0.5\columnwidth}
+ $E' = \{r/(0,1)^\omega, r/(1,2)^\omega\}$. \\
+ There is no linearization of the write operation able to justify $r/(0,1)^\omega$.
+ \end{columns}
+ \end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/forte.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/forte.tex
new file mode 100644
index 0000000000000000000000000000000000000000..00b15b6231fb0c31840eb8a5bacc684ffe0af6d2
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/forte.tex
@@ -0,0 +1,45 @@
+\begin{frame}
+ \frametitle{Safety}
+ \begin{block}{Definition}
+ Each \textbf{read} operation made in the same \textbf{non-competitor} context provide the same result.
+ \end{block}
+ \begin{figure}
+ \input{schemas/linearisation_surete_hc}
+ \end{figure}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Regularity}
+ \begin{block}{Definition}
+ An \textbf{reading operation concurrent with a writing operation} must provide the value \textbf{before or after the write}.
+ \end{block}
+ \begin{figure}
+ \input{schemas/linearisation_regularite_hc}
+ \end{figure}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Atomicity}
+ \begin{block}{Definition}
+ If \textbf{two reading are non-competitor}, the second one must provide a value \textbf{at least as recent as} the previous one.
+ \end{block}
+ \begin{figure}
+ \input{schemas/linearisation_atomicite_hc}
+ \end{figure}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Atomic Consistency ($C_\top$)}
+
+ \begin{block}{Définition}
+ Atomic consistency is the stronger consistency class.
+ \begin{itemize}
+ \item Provide an awful interactivity.
+ \item Need a strong synchronization between each operation.
+ \begin{itemize}
+ \item Each read or write operation lock the others and need to wait the realease from the previous one.
+ \end{itemize}
+ \item He's used as a reference for the other consistency class.
+ \end{itemize}
+ \end{block}
+ \end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/index.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/index.tex
new file mode 100644
index 0000000000000000000000000000000000000000..8bc1bda57db7ee7a324634a14d59339a9d586c4e
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/consistency/index.tex
@@ -0,0 +1,8 @@
+\subsection{Strong consistency}
+\include{consistency/forte.tex}
+
+\subsection{The compromises of the strong consistency}
+\include{consistency/faible.tex}
+
+\subsection{In a malicious context ?}
+\include{consistency/byzantin.tex}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/bases.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/bases.tex
new file mode 100644
index 0000000000000000000000000000000000000000..5bad156d406d08bd5c17ba201eb36d9c00f49dd7
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/bases.tex
@@ -0,0 +1,32 @@
+\begin{frame}
+ \frametitle{A distributed system}
+
+ \begin{block}{Definition}
+ A distributed system is a group of \textbf{actors} able to comunicate \textbf{each-other} working together to \textbf{complete a common task}.
+ \end{block}
+
+ % Schéma d'un système distribué
+
+ The system we consider on this presentation is a \textbf{asynchronous message-passing} system.
+
+\end{frame}
+
+\begin{frame}
+ \frametitle{A distributed system is a living system}
+
+ A distributed system changes over time.
+
+ There's some way to study these changes :
+ \begin{itemize}
+ \item focus on the \textbf{churn} (node addition and removal).
+ \item focus on the \textbf{messages}.
+ \item focus on the \textbf{connectedness}.
+ \item focus on the \textbf{states}. $\Leftarrow$
+ \item probably more... ?
+ \end{itemize}
+
+ The study of the state changes is also called the study of \textbf{consistency}.
+
+ \textbf{A small exemple}: A peer-to-peer discussion
+
+\end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/index.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/index.tex
new file mode 100644
index 0000000000000000000000000000000000000000..ffbbf9fc512f289ef5f02d1a1d157b82f21c6eb9
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/index.tex
@@ -0,0 +1,2 @@
+\subsection{Définition}
+\include{distr_sys/bases}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/images/carte_criteres.png b/docs/presentations/LIS/DALGO_6_juillet_2023/images/carte_criteres.png
new file mode 100755
index 0000000000000000000000000000000000000000..cd71ddc88a22310aca2c4ce1557e5b6debbdc910
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diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/intro/index.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/index.tex
new file mode 100644
index 0000000000000000000000000000000000000000..8debf0ea51b861984896e7d20b08f4e3cd4a879b
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/index.tex
@@ -0,0 +1,5 @@
+\subsection{Introduction}
+\include{intro/presentation.tex}
+
+\subsection{My internship}
+\include{intro/suite.tex}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/intro/presentation.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/presentation.tex
new file mode 100644
index 0000000000000000000000000000000000000000..939997423e104664b7d3d35c3b80eb1a6d3a03df
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/presentation.tex
@@ -0,0 +1,16 @@
+\begin{frame}
+ \frametitle{Présentation}
+
+ \begin{itemize}
+ \item Amaury JOLY
+ \item Master Informatique
+ \begin{itemize}
+ \item Option Fiabilité Sécurité Informatique (FSI)
+ \end{itemize}
+
+ \end{itemize}
+
+
+
+
+\end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/intro/suite.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/suite.tex
new file mode 100644
index 0000000000000000000000000000000000000000..29746d62230a1031230728765fcaab8c1dd671af
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/intro/suite.tex
@@ -0,0 +1,18 @@
+\begin{frame}
+ \frametitle{My Internship}
+
+ \begin{itemize}
+ \item Begin in april
+ \item Collaboration between Parsec and LIS-LAB
+ \begin{itemize}
+ \item Parsec is a for-profit organization working on an open-source software named Parsec
+ \item It's a software architecture to file sharing with E2EE in a zero-trust approach
+ \end{itemize}
+ \item Parsec want to add Collaborative Editing on their products:
+ \begin{itemize}
+ \item With a zero-trust approach (so probably decentralized)
+ \item With a high avaibility and low latency approach
+ \end{itemize}
+ \item Subject is \textit{Weak Consistency Byzantin Fault Tolerent}
+ \end{itemize}
+\end{frame}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/main.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/main.tex
new file mode 100755
index 0000000000000000000000000000000000000000..e8df4584fec69644d1b0955038564d8449a0fe93
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/main.tex
@@ -0,0 +1,60 @@
+\documentclass{beamer}
+\usetheme{Boadilla}
+\usecolortheme{orchid}
+
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage[french]{babel}
+\usepackage{stackengine}
+
+\addtobeamertemplate{navigation symbols}{}{%
+ \usebeamerfont{footline}%
+ \usebeamercolor[fg]{footline}%
+ \hspace{1em}%
+ \insertframenumber/\inserttotalframenumber
+}
+\usepackage{ulem}
+\usepackage{tkz-tab}
+\setbeamertemplate{blocks}[rounded]%
+[shadow=true]
+\AtBeginSection{%
+ \begin{frame}
+ \tableofcontents[sections=\value{section}]
+ \end{frame}
+}
+
+\usepackage{tikz}
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usetikzlibrary{arrows.meta}
+
+\usepackage{tcolorbox}
+
+\title[bwconsistency]{Étude de la cohérence dans les systèmes distribués}
+\subtitle{Journée DALGO}
+\author[JOLY Amaury]{JOLY Amaury\\ \textbf{Encadrants :} GODARD Emmanuel, TRAVERS Corentin }
+% \\[2ex] \includegraphics[scale=0.1]{./img/amu.png}
+\institute[LIS, Scille]{LIS-LAB, Scille}
+\date{6 juillet 2023}
+
+\begin{document}
+
+\maketitle
+
+\begin{frame}{Table des matières}
+ \tableofcontents
+\end{frame}
+
+\section{Introduction}
+\input{intro/index.tex}
+
+\section{Distributed systems and consistency}
+\input{distr_sys/index.tex}
+
+\section{The compromises of consistency}
+\input{consistency/index.tex}
+
+\section{What's next ?}
+\input{conclusion/index.tex}
+
+\end{document}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/ccv_hc_1.png b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/ccv_hc_1.png
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index 0000000000000000000000000000000000000000..a115a993db734be10d3382f589b15af6e77c8346
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diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_1.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_1.tex
new file mode 100755
index 0000000000000000000000000000000000000000..9217952ba1d5537ef1881f1abdb0627193ec35e0
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_1.tex
@@ -0,0 +1,41 @@
+\resizebox{\columnwidth}{!}{
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$I(a)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(0,1)$};
+ \node[roundnode] (14) [right=35pt of 13] {};
+ \node[above] at (14.north) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+ \draw[arrow] (13) -- (14);
+
+ \node[roundnode] (21) [below=10pt of 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[below] at (22.south) {$R/\emptyset$};
+ \node[roundnode] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(0,2)$};
+ \node[roundnode] (24) [right=35pt of 23] {};
+ \node[below] at (24.south) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+ \draw[arrow] (23) -- (24);
+
+ \draw (24) -- (14);
+
+ \draw[dashed] ($(14)!0.5!(13) + (0,1)$) -- ++(0, -2.9);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_2.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_2.tex
new file mode 100755
index 0000000000000000000000000000000000000000..bd97baac1bef67b2ba4c07f2e636f626383fb9be
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/convergence_hc_2.tex
@@ -0,0 +1,41 @@
+\resizebox{\columnwidth}{!}{
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$I(a)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(0,1)$};
+ \node[roundnode] (14) [right=35pt of 13] {};
+ \node[above] at (14.north) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+ \draw[arrow] (13) -- (14);
+
+ \node[roundnode] (21) [below=10pt of 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[below] at (22.south) {$R/\emptyset$};
+ \node[roundnode] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(0,2)$};
+ \node[roundnode] (24) [right=35pt of 23] {};
+ \node[below] at (24.south) {$r/(2,1)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+ \draw[arrow] (23) -- (24);
+
+ \draw (24) -- (14);
+
+ \draw[dashed] ($(14)!0.5!(13) + (0,1)$) -- ++(0, -2.9);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_atomicite_hc.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_atomicite_hc.tex
new file mode 100755
index 0000000000000000000000000000000000000000..72e4f57d12447f03ceece6b869624284d46701b4
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_atomicite_hc.tex
@@ -0,0 +1,26 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundedrectangle/.style={draw, rounded corners, rectangle, minimum height=10pt, minimum width=20pt},
+ invisible/.style={draw=none, fill=none},
+ ]
+
+ \node[invisible] (10) {};
+ \node[roundedrectangle, minimum width=150pt] (11) [right=100pt of 10] {$w_x(1)$};
+ \node[invisible] (12) [right=100pt of 11] {};
+
+ \node[invisible] (20) [below=15pt of 10] {};
+ \node[roundedrectangle, minimum width=50pt] (21) [right=25pt of 20] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (22) [right=75pt of 21] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (23) [right=75pt of 22] {\textcolor{red}{$r/(1)$}};
+ \node[invisible] (24) [below=15pt of 12] {};
+
+ \node[invisible] (30) [below=15pt of 20] {};
+ \node[roundedrectangle, minimum width=50pt] (31) [right=125pt of 30] {\textcolor{red}{$r/(1)$}};
+ \node[roundedrectangle, minimum width=50pt] (32) [right=40pt of 31] {\textcolor{red}{$r/(1)$}};
+ \node[invisible] (33) [below=15pt of 24] {};
+
+ \draw (10) -- (11) -- (12);
+ \draw (20) -- (21) -- (22) -- (23) -- (24);
+ \draw (30) -- (31) -- (32) -- (33);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_regularite_hc.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_regularite_hc.tex
new file mode 100755
index 0000000000000000000000000000000000000000..281227c8f4ec1cb665dee3176496f0d6bbefd7c3
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_regularite_hc.tex
@@ -0,0 +1,26 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundedrectangle/.style={draw, rounded corners, rectangle, minimum height=10pt, minimum width=20pt},
+ invisible/.style={draw=none, fill=none},
+ ]
+
+ \node[invisible] (10) {};
+ \node[roundedrectangle, minimum width=150pt] (11) [right=100pt of 10] {$w_x(1)$};
+ \node[invisible] (12) [right=100pt of 11] {};
+
+ \node[invisible] (20) [below=15pt of 10] {};
+ \node[roundedrectangle, minimum width=50pt] (21) [right=25pt of 20] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (22) [right=75pt of 21] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (23) [right=75pt of 22] {\textcolor{red}{$r/(1)$}};
+ \node[invisible] (24) [below=15pt of 12] {};
+
+ \node[invisible] (30) [below=15pt of 20] {};
+ \node[roundedrectangle, minimum width=50pt] (31) [right=125pt of 30] {\textcolor{red}{$r/(1)$}};
+ \node[roundedrectangle, minimum width=50pt] (32) [right=40pt of 31] {\textcolor{blue}{$r/(0)$}};
+ \node[invisible] (33) [below=15pt of 24] {};
+
+ \draw (10) -- (11) -- (12);
+ \draw (20) -- (21) -- (22) -- (23) -- (24);
+ \draw (30) -- (31) -- (32) -- (33);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_surete_hc.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_surete_hc.tex
new file mode 100755
index 0000000000000000000000000000000000000000..fde5f3ac26c14e208b73ae61034cc31875129839
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/linearisation_surete_hc.tex
@@ -0,0 +1,26 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundedrectangle/.style={draw, rounded corners, rectangle, minimum height=10pt, minimum width=20pt},
+ invisible/.style={draw=none, fill=none},
+ ]
+
+ \node[invisible] (10) {};
+ \node[roundedrectangle, minimum width=150pt] (11) [right=100pt of 10] {$w_x(1)$};
+ \node[invisible] (12) [right=100pt of 11] {};
+
+ \node[invisible] (20) [below=15pt of 10] {};
+ \node[roundedrectangle, minimum width=50pt] (21) [right=25pt of 20] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (22) [right=75pt of 21] {\textcolor{blue}{$r/(0)$}};
+ \node[roundedrectangle, minimum width=50pt] (23) [right=75pt of 22] {\textcolor{red}{$r/(1)$}};
+ \node[invisible] (24) [below=15pt of 12] {};
+
+ \node[invisible] (30) [below=15pt of 20] {};
+ \node[roundedrectangle, minimum width=50pt] (31) [right=125pt of 30] {\textcolor{red!50!blue}{$r/(27)$}};
+ \node[roundedrectangle, minimum width=50pt] (32) [right=40pt of 31] {\textcolor{red}{$r/(1)$}};
+ \node[invisible] (33) [below=15pt of 24] {};
+
+ \draw (10) -- (11) -- (12);
+ \draw (20) -- (21) -- (22) -- (23) -- (24);
+ \draw (30) -- (31) -- (32) -- (33);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_1.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_1.tex
new file mode 100755
index 0000000000000000000000000000000000000000..f61f58c41ebcc5de8945cc2273651aee06e9d1f9
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_1.tex
@@ -0,0 +1,34 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode, draw=red, fill=red] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode, draw=blue, fill=blue] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(0,0)$};
+ \node[roundnode, draw=blue, fill=blue] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(0,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode, draw=blue, fill=blue] (21) [below=10pt of 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode, draw=red, fill=red] (22) [right=of 21] {};
+ \node[below] at (22.south) {$r/(0,0)$};
+ \node[roundnode, draw=red, fill=red] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(0,1)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+
+ \draw[message] (11) -- ($(22)!0.5!(23)$);
+ \draw[message] (21) -- ($(12)!0.5!(13)$);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_2.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_2.tex
new file mode 100755
index 0000000000000000000000000000000000000000..399824863b54a92dbbdf0a2d2d3895f755352feb
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/localiteetat_hc_2.tex
@@ -0,0 +1,32 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(0,0)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(0,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode] (21) [below=10pt of 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[below] at (22.south) {$r/(0,1)$};
+ \node[roundnode] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(2,1)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_1.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_1.tex
new file mode 100755
index 0000000000000000000000000000000000000000..1875a6bf62520d605f5a8840f2436cad3d8a10fb
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_1.tex
@@ -0,0 +1,31 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(0,1)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(2,1)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode] (21) [below=10pt of 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[below] at (22.south) {$r/(0,2)$};
+ \node[roundnode] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_2.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_2.tex
new file mode 100755
index 0000000000000000000000000000000000000000..4aaec996612e76ff0bdbde947f98cae240dde0e3
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/validite_hc_2.tex
@@ -0,0 +1,31 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[left] at (11.west) {$p_0$};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(0,1)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(0,1)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode] (21) [below=10ptof 11] {};
+ \node[left] at (21.west) {$p_1$};
+ \node[below] at (21.south) {$w(2)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[below] at (22.south) {$r/(0,2)$};
+ \node[roundnode] (23) [right=of 22] {};
+ \node[below] at (23.south) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (21) -- (22);
+ \draw[arrow] (22) -- (23);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_1.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_1.tex
new file mode 100755
index 0000000000000000000000000000000000000000..839acb39b344485ead69853f030c84eeaa958fd5
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_1.tex
@@ -0,0 +1,42 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode, color=red] (11) {};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode, color=red!50] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(0,1)$};
+ \node[roundnode, color=red!25] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(3,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode, color=green!75!black] (21) [below=20pt of 11] {};
+ \node[left] at (21.west) {$r/(3,1)$};
+ \node[roundnode, color=green!95!black] (22) [right=of 21] {};
+ \node[right] at (22.east) {$w(2)$};
+
+ \draw[arrow] (21) -- (22);
+
+ \node[roundnode, color=blue] (31) [below=20pt of 21] {};
+ \node[below] at (31.south) {$w(3)$};
+ \node[roundnode, color=blue!50] (32) [right=of 31] {};
+ \node[below] at (32.south) {$r/(3,1)$};
+ \node[roundnode, color=blue!25] (33) [right=of 32] {};
+ \node[below] at (33.south) {$r/(3,2)^\omega$};
+
+ \draw[arrow] (31) -- (32);
+ \draw[arrow] (32) -- (33);
+
+ \draw[message] (11) -- (21);
+ \draw[message] (31) -- (21);
+ \draw[message] (21) -- (32);
+ \draw[message] (22) -- (13);
+ \draw[message] (22) -- (33);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_2.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_2.tex
new file mode 100755
index 0000000000000000000000000000000000000000..1651ec276644c6fe8215f42d36415325f0862298
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_2.tex
@@ -0,0 +1,29 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode] (11) {};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(2,1)$};
+ \node[roundnode] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(2,1)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode] (21) [below=20pt of 11] {};
+ \node[left] at (21.west) {$r/(0,1)$};
+ \node[roundnode] (22) [right=of 21] {};
+ \node[right] at (22.east) {$w(2)$};
+
+ \draw[arrow] (21) -- (22);
+
+ \draw[message] (11) -- (21);
+ \draw[message] (22) -- (12);
+ \end{tikzpicture}
+}
\ No newline at end of file
diff --git a/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_3.tex b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_3.tex
new file mode 100755
index 0000000000000000000000000000000000000000..6b109f93d2aae008ad50ecde8eb4b836ca2b0b82
--- /dev/null
+++ b/docs/presentations/LIS/DALGO_6_juillet_2023/schemas/wcc_hc_3.tex
@@ -0,0 +1,41 @@
+\resizebox{\columnwidth}{!}{%
+ \begin{tikzpicture}[
+ roundnode/.style={circle, draw=black, fill=black, very thick, minimum size=1pt,},
+ ignorednode/.style={circle, draw=black!20, fill=black!20, very thick, minimum size=1pt,},
+ arrow/.style={|->, thick,},
+ message/.style={->, blue!50, dashed, -{Circle[length=4pt,]}},
+ ]
+
+ \node[roundnode, color=red] (11) {};
+ \node[above] at (11.north) {$w(1)$};
+ \node[roundnode, color=red!50] (12) [right=of 11] {};
+ \node[above] at (12.north) {$r/(3,1)$};
+ \node[roundnode, color=red!25] (13) [right=of 12] {};
+ \node[above] at (13.north) {$r/(1,2)^\omega$};
+
+ \draw[arrow] (11) -- (12);
+ \draw[arrow] (12) -- (13);
+
+ \node[roundnode, color=green!75!black] (21) [below=20pt of 11] {};
+ \node[left] at (21.west) {$r/(0,0)$};
+ \node[roundnode, color=green!95!black] (22) [right=of 21] {};
+ \node[right] at (22.east) {$w(2)$};
+
+ \draw[arrow] (21) -- (22);
+
+ \node[roundnode, color=blue] (31) [below=20pt of 21] {};
+ \node[below] at (31.south) {$w(3)$};
+ \node[roundnode, color=blue!50] (32) [right=of 31] {};
+ \node[below] at (32.south) {$r/(1,3)$};
+ \node[roundnode, color=blue!25] (33) [right=of 32] {};
+ \node[below] at (33.south) {$r/(3,2)^\omega$};
+
+ \draw[arrow] (31) -- (32);
+ \draw[arrow] (32) -- (33);
+
+ \draw[message] (11) -- (31);
+ \draw[message] (31) -- (12);
+ \draw[message] (22) -- (13);
+ \draw[message] (22) -- (33);
+ \end{tikzpicture}
+}
\ No newline at end of file