diff --git a/recherches/ALDLoverAB/ABAL.pdf b/recherches/ALDLoverAB/ABAL.pdf
new file mode 100644
index 0000000..66b9554
Binary files /dev/null and b/recherches/ALDLoverAB/ABAL.pdf differ
diff --git a/recherches/ALDLoverAB/algo/index.tex b/recherches/ALDLoverAB/algo/index.tex
new file mode 100644
index 0000000..4c882e3
--- /dev/null
+++ b/recherches/ALDLoverAB/algo/index.tex
@@ -0,0 +1,46 @@
+We define $k$ as the id of the round \\
+the $getMax(..)$ function able to return the highest round played in the system.
+
+\begin{algorithm}[H]
+\DontPrintSemicolon
+\SetAlgoLined
+\KwIn{le message $m$}
+\BlankLine
+\While{true}{
+ proves = READ() \\
+ k = getMax(dump) + 1 \\
+ APPEND(k || m) \\
+ \If{PROVE(k)}{
+ APPEND(k) \\
+ return
+ }
+}
+\caption{AB\_Broadcast}
+\end{algorithm}
+
+We define $k\_max$ as an intager \\
+$getMax(..)$ function able to return the highest round played in the system. \\
+% $proves_r$ as the sub set of proves with only the valid proves associated to the round r \\
+$proves_r \subseteq proves$ s.a. $\forall PROVE(x) \in proves_r$, x is in the form $r || m$ with $m$ who cannot be empty \\
+$proves_r^i$ is the $PROVE(r || m )$ operation submited by the process i if exist \\
+
+\begin{algorithm}[H]
+ \DontPrintSemicolon
+ \SetAlgoLined
+ \BlankLine
+ \While{true}{
+ proves = READ() \\
+ k\_max = getMax(proves) \\
+ \For{r=k+1 \emph{\KwTo} k\_max}{
+ APPEND(r)\\
+ $proves_r$ = \{$\forall i, PROVE(r)_i \in READ()$\} \\
+ \For{i = 1 \emph{\KwTo} $|P|$}{
+ \If{$\exists PROVE(r)_i \in proves_r$}{
+ AB\_Recv($m$ s.t. $PROVE(r || m) \in proves$)
+ }
+ }
+ }
+ }
+
+ \caption{AB\_Listen}
+\end{algorithm}
\ No newline at end of file
diff --git a/recherches/ALDLoverAB/intro/index.tex b/recherches/ALDLoverAB/intro/index.tex
new file mode 100644
index 0000000..81a78a7
--- /dev/null
+++ b/recherches/ALDLoverAB/intro/index.tex
@@ -0,0 +1,61 @@
+
+\subsubsection{Model Properties}
+
+The model is defined as Message-passing Aysnchronous. \\
+There is n process. Each process is associated to a unique unforgeable id $i$.\\
+Each process know the identity of all the process in the system\\
+Each process have a reliable communication channel with all the others process such as:
+\begin{itemize}
+ \item send(m) is the send primitive
+ \item recv(m) is the reception primitive
+\end{itemize}
+A message send is eventualy received\\
+The system is Crash-Prone. There is at most f process who can crash such as f < n.\\
+
+
+\subsubsection{AtomicBroadcast Properties}
+
+\begin{theorem}{AB\_broadcast Validity}
+ if a message is sent by a correct process, the message is eventually received by all the correct process.
+\end{theorem}
+
+\begin{theorem}{AB\_receive Validity}
+ if a message is received by a correct process, the message is eventually received by all the correct process.
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety No creation}
+ if a message is received by a correct process, the message was emitted by a correct porcess.
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety No duplication}
+ each message is received at most 1 time by each process.
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety Ordering}
+ $\forall m_1, m_2$ two messages, $\forall p_i, p_j$ two process. \\
+ if AB\_recv(m1) and AB\_recv(m2) for $p_i, p_j$ \\
+ and AB\_recv(m1) is before AB\_recv(m2) for $p_i$ \\
+ so AB\_recv(m1) is before AB\_recv(m2) for $p_j$ \\
+\end{theorem}
+
+
+
+\subsubsection{DenyList Properties}
+
+\begin{theorem}{APPEND Validity}
+ a APPEND(x) is valid iff the process p who sent the operation is such as $p \in \Pi_M$.
+ And iff $x \in S$ where S is a set of valid values.
+\end{theorem}
+
+\begin{theorem}{PROVE Validity}
+ a PROVE(x) is valid iff the process $p$ who sent the operation is such as $p \in \Pi_V$.
+ And iff $\exists$ APPEND(x) who appears before PROVE(x) in Seq.
+\end{theorem}
+
+\begin{theorem}{PROGRESS}
+ if an APPEND(x) is invoked, so there is a point in the linearization of the operations such as all PROVE(x) are valids.
+\end{theorem}
+
+\begin{theorem}{READ Validity}
+ READ() return a list of tuples who is a random permutation of all valids PROVE() associated to the identity of the emiter process.
+\end{theorem}
\ No newline at end of file
diff --git a/recherches/ALDLoverAB/main.aux b/recherches/ALDLoverAB/main.aux
new file mode 100644
index 0000000..8a52018
--- /dev/null
+++ b/recherches/ALDLoverAB/main.aux
@@ -0,0 +1,20 @@
+\relax
+\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
+\@nameuse{bbl@beforestart}
+\catcode `:\active
+\catcode `;\active
+\catcode `!\active
+\catcode `?\active
+\abx@aux@refcontext{nty/global//global/global/global}
+\providecommand \oddpage@label [2]{}
+\babel@aux{french}{}
+\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Model}{1}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Model Properties}{1}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}AtomicBroadcast Properties}{1}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}DenyList Properties}{1}{}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Algorithms}{1}{}\protected@file@percent }
+\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces AB\_Broadcast}}{2}{}\protected@file@percent }
+\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces AB\_Listen}}{2}{}\protected@file@percent }
+\abx@aux@read@bbl@mdfivesum{76D65A242EC496C9B4361AF646FF12CB}
+\gdef \@abspage@last{3}
diff --git a/recherches/ALDLoverAB/main.bbl b/recherches/ALDLoverAB/main.bbl
new file mode 100644
index 0000000..1b062e4
--- /dev/null
+++ b/recherches/ALDLoverAB/main.bbl
@@ -0,0 +1,20 @@
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+% $ biblatex bbl format version 3.3 $
+% Do not modify the above lines!
+%
+% This is an auxiliary file used by the 'biblatex' package.
+% This file may safely be deleted. It will be recreated by
+% biber as required.
+%
+\begingroup
+\makeatletter
+\@ifundefined{ver@biblatex.sty}
+ {\@latex@error
+ {Missing 'biblatex' package}
+ {The bibliography requires the 'biblatex' package.}
+ \aftergroup\endinput}
+ {}
+\endgroup
+
+\endinput
+
diff --git a/recherches/ALDLoverAB/main.bbl-SAVE-ERROR b/recherches/ALDLoverAB/main.bbl-SAVE-ERROR
new file mode 100644
index 0000000..1b062e4
--- /dev/null
+++ b/recherches/ALDLoverAB/main.bbl-SAVE-ERROR
@@ -0,0 +1,20 @@
+% $ biblatex auxiliary file $
+% $ biblatex bbl format version 3.3 $
+% Do not modify the above lines!
+%
+% This is an auxiliary file used by the 'biblatex' package.
+% This file may safely be deleted. It will be recreated by
+% biber as required.
+%
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+\@ifundefined{ver@biblatex.sty}
+ {\@latex@error
+ {Missing 'biblatex' package}
+ {The bibliography requires the 'biblatex' package.}
+ \aftergroup\endinput}
+ {}
+\endgroup
+
+\endinput
+
diff --git a/recherches/ALDLoverAB/main.bcf b/recherches/ALDLoverAB/main.bcf
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diff --git a/recherches/ALDLoverAB/main.synctex.gz b/recherches/ALDLoverAB/main.synctex.gz
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+\documentclass{article}
+
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+\usepackage[utf8]{inputenc}
+\usepackage{csquotes}
+\usepackage[french]{babel}
+\usepackage[affil-it]{authblk}
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+
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+
+\newtheorem{theorem}{Property}
+
+\addbibresource{sources.bib}
+
+\begin{document}
+
+\title{???}
+\author{JOLY Amaury \\ \textbf{Encadrants :} GODARD Emmanuel, TRAVERS Corentin}
+\affil{Aix-Marseille Université, Scille}
+\date{\today}
+
+\begin{titlepage}
+ \maketitle
+\end{titlepage}
+
+
+\section{Introduction}
+
+\subsection{Model}
+\input{intro/index.tex}
+
+\subsection{Algorithms}
+\input{algo/index.tex}
+
+\printbibliography
+
+
+\end{document}
\ No newline at end of file
diff --git a/recherches/ALDLoverAB/sources.bib b/recherches/ALDLoverAB/sources.bib
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