edit presentation dalgo + gitignore latex

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}

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}

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}

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}

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}

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}

docs/presentations/LIS/DALGO_6_juillet_2023/distr_sys/index.tex

@@ -0,0 +1,2 @@
+\subsection{Définition}
+\include{distr_sys/bases}

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}

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}

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}

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}

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}
+}

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,},
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+        ]
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+        \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);
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+        \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}
+}

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},
+        ]
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+        \node[invisible] (10) {};
+        \node[roundedrectangle, minimum width=150pt] (11) [right=100pt of 10] {$w_x(1)$};
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+        \node[invisible] (20) [below=15pt of 10] {};
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+        \node[invisible] (33) [below=15pt of 24] {};
+
+        \draw (10) -- (11) -- (12);
+        \draw (20) -- (21) -- (22) -- (23) -- (24);
+        \draw (30) -- (31) -- (32) -- (33);
+    \end{tikzpicture}
+}

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},
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+        \node[invisible] (33) [below=15pt of 24] {};
+
+        \draw (10) -- (11) -- (12);
+        \draw (20) -- (21) -- (22) -- (23) -- (24);
+        \draw (30) -- (31) -- (32) -- (33);
+    \end{tikzpicture}
+}

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},
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+        \node[invisible] (33) [below=15pt of 24] {};
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+        \draw (10) -- (11) -- (12);
+        \draw (20) -- (21) -- (22) -- (23) -- (24);
+        \draw (30) -- (31) -- (32) -- (33);
+    \end{tikzpicture}
+}

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,},
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+        \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);
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+        \node[roundnode, draw=blue, fill=blue] (21) [below=10pt of 11] {};
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+        \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}
+}

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}
+}

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}
+}

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}
+}

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}
+}

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}
+}

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}
+}