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## Allow List over PC
### Modele
**Base de Mathieu**
Soit $\\Pi$ l'ensemble des processus $p_1, ... p_N$
$\\Pi_M \\subseteq \\Pi$ les processus autorisés à $APPEND(x)$
$\\Pi_V \\subseteq \\Pi$ les processus autorisés à $PROVE(x)$
Chaque processus est séquentiel mais le système est asynchrone (le $\\Delta$ de vitesse d'horloge relative est inconnue par les processus) Le système est crash prône
Tous les processus ont un identifiant et les IDs sont connues de tous les processus.
**Spécificité Message-Passing**
2 opérations possibles:
- $send(O, p_i)$
- $recv(O, p_i)$
$H$ l'ensemble des séquences d'opérations $H|p_i$ les opérations relatives à $p_i$ $H|x$ l'ensemble des séquences d'opérations relatives à l'objet $x$ Les processus peuvent être byzantin en ne suivant pas le protocole définit. On admet que la transmission des message respecte les propriétés de reliable broadcast. C'est a dire que tous les messages envoyés sont reçu par tous. Et que pour deux message envoyé dans un ordre précis par un même processus ils seront reçu dans ce même ordre par tous les autres processus.
### Problematique
$O$ ensemble des types d'opérations :
- $APPEND(x)$
- $PROVE(x)$
- $READ()$
On veut remplir les propriétés suivantes :
- Termination: toutes les opérations terminent par un "return"
- APPEND validity: Un APPEND(x) est valide ssi $\\forall p_i$ t.q. $send(APPEND(x)) \\in H| p_i$. $p_i \\in \\Pi_M \\subseteq \\Pi$
- PROVE validity: Un PROVE(x) est valide ssi $\\forall p_i$ t.q. $send(PROVE(x)) \\in H| p_i$. $p_i \\in \\Pi_V \\subseteq \\Pi$ ET un $APPEND(x)$ apparait dans $\\Pi_V$
- Progress: si un $APPPEND(x)$ est valide alors il exist $\\forall p_i$ un point dans $H|p_i$ tel que tous les $PROVE(x)$ sont valident.
- READ validity: $\\forall p_i$ l'opération $READ()$ doit retourner toutes les opérations $PROVE(...) \\in H|p_i$
### Algo
```
appends a set of objetcs
proves a set of tuples of (objetc, process id)
recv(APPEND(x), p_j)
if p_j \in \Pi_M
appends += x
return
recv(PROVE(x), p_j)
if p_j \in \Pi_V
if x \in appends
proves += (x, p_j)
return
APPEND()
if p_i \in \Pi_V
appends += x
send(APPEND(x), p_i)
return
PROVE(x)
if p_i \in \Pi_M
if x \in appends
proves += (x, p_i)
send(PROVE(x), p_i)
return
READ()
return proves
```
### Preuve
**Termination**
Toutes les fonctions sont séquentiels et synchrones. Il n'y a aucune boucle, les fonctions terminent forcements.
**APPEND Validity**
La condition `if p_j \in \Pi_M` dans la fonction APPEND(x) garantit qu'aucun processus légitime ne peut ajouter d’élément dans la whitelist si il n'est pas manageur. Cette même condition dans recv(APPEND(x)) garantit qu'aucun processus légitime n'acceptera d'ajout d'élément soumis par un processus non manageur. Cette garantit repose sur le fait que les identifiants sont infalsifiables.
**PROVE Validity**
La condition `if p_j \in \Pi_V` dans la fonction PROVE(x) garantit qu'aucun processus légitime ne peut ajouter d’élément dans la whitelist si il n'est pas validateur. Cette même condition dans recv(PROVE(x)) garantit qu'aucun processus légitime n'acceptera d'ajout d'élément soumis par un processus non validateur. Cette garantit repose sur le fait que les identifiants sont infalsifiables.
De même la condition `if x \in appends` dans PROVE(x) assure que le processus courant a déjà reçu ou émis lui même un APPEND(x), puisque la seule manière d'ajouter un élément a l’ensemble `appends` est via les fonctions recv(APPEND(x)) et APPEND(x) une fois que les conditions de APPEND Validity sont respectés. De la même manière cette condition dans recv(PROVE(x)) assure qu'une requête PROVE(x) envoyé par un validateur malveillant ne faisant pas suite à un APPEND(x) ne soit pas considéré par les processus légitimes.
**PROGRESS**
Étant donné que tout message est eventually reçu. Tout APPEND(x) valide sera envoyé via la fonction `send` et sera reçu dans un temps $\\delta t$ par tous les processus. Avec $\\delta t$ étant le temps de transmission le plus long entre deux processus. Cette borne supérieur $\\delta t$ peut etre définit dans un système synchrone en admettant une borne maximal pour la transmission la plus lente entre deux `p`. Assurant ainsi que chaque APPEND(x) valide sera considéré par l'ensemble du système à $t + \\delta t$.
Cependant dans un système asynchrone ce $\\delta t$ est par définition non définit, rendent la propriété de PROGRESS insatisfaisable.
**READ Validity**
Pour ce point il convient de démontrer que tout tuple dans proves se trouve bien dans $\\forall PROVE(..) \\in H|p_i$ tel que $p_i$ le processus invoquant le READ. L'ajout a l'ensemble proves dépend des fonctions PROVE() et recv(PROVE()).
Dans ces deux fonctions on assure déjà la validité des PROVE pour $p_i$. Tout PROVE valide reçu ou émis par p_i est donc ajouté dans proves, ce qui correspond bien aux opérations proves de $H|p_i$.
## Deny List over PC
### Modele
__Base de Mathieu__
Soit $\\Pi$ l'ensemble des processus $p_1, ... p_N$
$\\Pi_M \\subseteq \\Pi$ les processus autorisés à $APPEND(x)$
$\\Pi_V \\subseteq \\Pi$ les processus autorisés à $PROVE(x)$
Chaque processus est séquentiel mais le système est asynchrone (le $\\Delta$ de vitesse d'horloge relative est inconnue par les processus) Le système est crash prône
Tous les processus ont un identifiant et les ids sont connues de tous les processus.
**Spécificité Message-Passing**
2 opérations possibles:
- $send(O, p_i)$
- $recv(O, p_i)$
$H$ l'ensemble des séquences d'opérations $H|p_i$ les opérations relatives à $p_i$ $H|x$ l'ensemble des séquences d'opérations relatives à l'objet $x$ Les processus peuvent être byzantin en ne suivant pas le protocole définit. On admet que la transmission des message respecte les propriétés de reliable broadcast. C'est a dire que tous les messages envoyés sont reçu par tous. Et que pour deux message envoyé dans un ordre précis par un même processus ils seront reçu dans ce même ordre par tous les autres processus.
### Problématique
$O$ ensemble des types d'opérations :
- $APPEND(x)$
- $PROVE(x)$
- $READ()$
On veut remplir les propriétés suivantes :
- Termination: toutes les opérations terminent par un "return"
- APPEND validity: Un APPEND(x) est valide ssi $\\forall p_i$ t.q. $send(APPEND(x)) \\in H| p_i$. $p_i \\in \\Pi_M \\subseteq \\Pi$
- PROVE validity: Un PROVE(x) est __invalid__ ssi $\\forall p_i$ t.q. $send(PROVE(x)) \\in H| p_i$. $p_i \\in \\Pi_V \\subseteq \\Pi$ ET un $APPEND(x)$ apparait dans $\\Pi_V$
- PROVE Anti-Flickering: Si une opération PROVE(x) invalide est soumise ou recu par un processus alors toutes les opérations PROVE(x) futur seront invalides
- READ validity: $\\forall p_i$ l'opération $READ()$ doit retourner toutes les opérations $PROVE(...) \\in H|p_i$
### Algo
```
appends a set of objetcs
proves a set of tuples of (objetc, process id)
recv(APPEND(x), p_j)
if p_j \in \Pi_M
appends += x
return
recv(PROVE(x), p_j)
if p_j \in \Pi_V
if x \neg\in appends
proves += (x, p_j)
return
APPEND()
if p_i \in \Pi_V
appends += x
send(APPEND(x), p_i)
return
PROVE(x)
if p_i \in \Pi_M
if x \neg\in appends
proves += (x, p_i)
send(PROVE(x), p_i)
return
READ()
return proves
```
### Preuve
**Termination**
Toutes les fonctions sont séquentiels et synchrones. Il n'y a aucune boucle, les fonctions terminent forcements.
**APPEND Validity**
La condition `if p_j \in \Pi_M` dans la fonction APPEND(x) garantit qu'aucun processus légitime ne peut ajouter d’élément dans la whitelist si il n'est pas manageur. Cette même condition dans recv(APPEND(x)) garantit qu'aucun processus légitime n'acceptera d'ajout d'élément soumis par un processus non manageur. Cette garantit repose sur le fait que les identifiants sont infalsifiables.
**PROVE Validity**
La condition `if p_j \in \Pi_V` dans la fonction PROVE(x) garantit qu'aucun processus légitime ne peut ajouter d’élément dans la whitelist si il n'est pas validateur. Cette même condition dans recv(PROVE(x)) garantit qu'aucun processus légitime n'acceptera d'ajout d'élément soumis par un processus non validateur. Cette garantit repose sur le fait que les identifiants sont infalsifiables.
De même la condition `if x \neg\in appends` dans PROVE(x) assure que le processus courant n'a pas déjà reçu ou émis lui même un APPEND(x), puisque la seule manière d'ajouter un élément a l’ensemble `appends` est via les fonctions recv(APPEND(x)) et APPEND(x) une fois que les conditions de APPEND Validity sont respectés.
De la même manière cette condition dans recv(PROVE(x)) assure qu'une requête PROVE(x) envoyé par un validateur malveillant faisant suite à un APPEND(x) ne soit pas considéré par les processus legéitimes.
**ANTI-FLICKERING**
Étant donné que tout message est eventually reçu. Tout APPEND(x) valide sera envoyé via la fonction `send` et sera reçu dans un temps $\\delta t$ par tous les processus. Avec $\\delta t$ étant le temps de transmission le plus long entre deux processus. Cette borne supérieur $\\delta t$ peut etre définit dans un système synchrone en admettant une borne maximal pour la transmission la plus lente entre deux `p`. Assurant ainsi que chaque APPEND(x) valide sera considéré par l'ensemble du système à $t + \\delta t$.
Cependant dans un système asynchrone ce $\\delta t$ est par définition non définit, rendent la propriété d'anti-flickring insatisfaisable.
__READ Validity__
Pour ce point il convient de démontrer que tout tuple dans proves se trouve bien dans l'ensemble $E$, tel que $\\forall e \\in E$, $e = PROVE(x)$ et tel que $H'|p_i$ l'ensemble des opérations reçu et émise avant l'opération $e$, alors $\\nexists e' \\in H'|p_i$ t.q. $e' = APPEND(x)$ avec $p_i$ le processus invoquant le READ.
L'ajout a l'ensemble proves dépend des fonctions PROVE() et recv(PROVE()). Dans ces deux fonctions on assure déjà la validité des PROVE pour $p_i$. Tout PROVE valide reçu ou émis par p_i est donc ajouté dans proves, ce qui correspond bien aux opérations proves de $H|p_i$.
## Discussion
Il est impossible d’implémenter une AllowList ou DenyList dans un système asynchrone, ce qui conditionne déjà notre model sur ce point. Les propriétés de PROGRESS et d'ANTIFLICKERING étant directement lié à ce point.
Les points facilitant la résolution de notre problème sont d'une part la présence du ReliableBroadcast et d'autre part d'un identifiant infalsifiable. Les deux points étant lié puisque nous pouvons admettre que le reliable broadcast peut aussi s'occuper de l'authentification des messages, et de leur non répudiabilité.
Un axe d'amélioration est donc d'affaiblir le reliable broadcast pour ça il faut définir les propriétés essentiels a l’exécution de notre algorithme.
### RB
- Non répudiabilité (une fois que le message ets envoyé il est impossible pour un processus de le nier)
- Tout message envoyé est recu par tout le monde(eventual delivery)
- Immutabilité du message une fois qu'il est émis

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We consider a set of processes communicating asynchronously over reliable point-to-point channels. Each process maintains the following shared variables:
\begin{itemize}
\item \textbf{received}: the set of messages received (but not yet delivered).
\item \textbf{delivered}: the set of messages that have been received, ordered, and delivered.
\item \textbf{prop[$r$][$j$]}: the proposal set of process $j$ at round $r$. It contains the set of messages that process $j$ claims to have received but not yet delivered at round $r$, concatenated with its newly broadcast message.
\item \textbf{proves}: the current content of the \texttt{DenyList} registry, accessible via the operation \texttt{READ()}. It returns a list of tuples $(j, \texttt{PROVE}(r))$, each indicating that process $j$ has issued a valid \texttt{PROVE} for round $r$.
\item \textbf{winner$^r$}: the set of processes that have issued a valid \texttt{PROVE} operation for round $r$.
\item \textbf{RB-cast}: a reliable broadcast primitive that satisfies the properties defined in Section~1.1.2.
\item \textbf{APPEND$(r)$}, \textbf{PROVE$(r)$}: operations that respectively insert (APPEND) and attest (PROVE) the participation of a process in round $r$ in the DenyList registry.
\item \textbf{READ()}: retrieves the current local view of valid operations (APPENDs and PROVEs) from the DenyList.
\item \textbf{ordered$(S)$}: returns a deterministic total order over a set $S$ of messages (e.g., via hash or lexicographic order).
\end{itemize}
\resetalgline
\begin{algorithm}
\vspace{1em}
\textbf{RB-received$(m, S, r_0, j_0)$}
\begin{algorithmic}[1]
\State \nextalgline $\textit{received} \gets \textit{received} \cup \{m\}$
\State \nextalgline $\textit{prop}[r_0][j_0] \gets S$
\end{algorithmic}
\vspace{1em}
\textbf{AB-broadcast$(m, j_0)$}
\begin{algorithmic}[1]
\State \nextalgline $\textit{proves} \gets \texttt{READ}()$
\State \nextalgline $r_0 \gets \max\{r : \exists j,\ (j, \texttt{PROVE}(r)) \in \textit{proves}\} + 1$
\State \nextalgline $\texttt{RB-cast}(m, (\textit{received} \setminus \textit{delivered}) \cup \{m\}, r_0, j_0)$
\State \nextalgline \texttt{PROVE}$(r_0)$
\State \nextalgline \texttt{APPEND}$(r_0)$
\Repeat
\State \nextalgline $\textit{proves} \gets \texttt{READ}()$
\State \nextalgline $r_1 \gets \max\{r : \exists j,\ (j, \texttt{PROVE}(r)) \in \textit{proves}\} - 1$
\State \nextalgline $\textit{winner}^{r_1} \gets \{j : (j, \texttt{PROVE}(r_1)) \in \textit{proves}\}$
\State \nextalgline \textbf{wait} $\forall j \in \textit{winner}^{r_1},\ \textit{prop}[r_1][j] \neq \bot$
\Until{\nextalgline $\exists r_2,\ \exists j_2 \in \textit{winner}^{r_2},\ m \in \textit{prop}[r_2][j_2]$} \nextalgline
\end{algorithmic}
\vspace{1em}
\textbf{AB-listen}
\begin{algorithmic}[1]
\While{true}
\State \nextalgline $\textit{proves} \gets \texttt{READ}()$
\State \nextalgline $r_1 \gets \max\{r : \exists j,\ (j, \texttt{PROVE}(r)) \in \textit{proves}\} - 1$
\For{$r_2 \in [r_0, \dots, r_1]$} \nextalgline
\State \nextalgline \texttt{APPEND}$(r_2)$
\State \nextalgline $\textit{proves} \gets \texttt{READ}()$
\State \nextalgline $\textit{winner}^{r_2} \gets \{j : (i, \texttt{PROVE}(r_2)) \in \textit{proves}\}$
\State \nextalgline \textbf{wait} $\forall j \in \textit{winner}^{r_2},\ \textit{prop}[r_2][j] \neq \bot$
\State \nextalgline $M^{r_2} \gets \bigcup_{j \in \textit{winner}^{r_2}} \textit{prop}[r_2][j]$
\ForAll{$m \in \texttt{ordered}(M^{r_2})$} \nextalgline
\State \nextalgline $\textit{delivered} \gets \textit{delivered} \cup \{m\}$
\State \nextalgline \texttt{AB-deliver}$(m)$
\EndFor
\EndFor
\EndWhile
\end{algorithmic}
\end{algorithm}

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\subsubsection{Model Properties}
The system consists of \textit{n} asynchronous processes communicating via reliable point-to-point message passing. \\
Each process has a unique, unforgeable identifier and knows the identifiers of all other processes. \\
Up to $f<n$ processes may crash (fail-stop). \\
The network is reliable: if a correct process sends a message to another correct process, it is eventually delivered. \\
Messages are uniquely identifiable: two messages sent by distinct processes or at different rounds are distinguishable \\
2 messages sent by the same processus in two differents rounds are differents \\
\begin{property}[Message Uniqueness]
If two messages are sent by different processes, or by the same process in different rounds, then the messages are distinct. \\
Formally : \\
\[
\forall p_1, p_2,\ \forall r_1, r_2,\ \forall m_1, m_2,\
\left(
\begin{array}{l}
\text{send}(p_1, r_1, m_1) \land \text{send}(p_2, r_2, m_2) \\
\land\ (p_1 \ne p_2 \lor r_1 \ne r_2)
\end{array}
\right)
\Rightarrow m_1 \ne m_2
\]
\end{property}
\subsubsection{Reliable Broadcast Properties}
\begin{property}{Integrity}
Every message received was previously sent. \\
Formally : \\
$\forall p_i : \text{bc-recv}_i(m) \Rightarrow \exists p_j : \text{bc-send}_j(m)$
\end{property}
\begin{property}{No Duplicates}
No message is received more than once at any single processor. \\
Formally : \\
$\forall m, \forall p_i: \text{bc-recv}_i(m) \text{ occurs at most once}$ \\
\end{property}
\begin{property}{Validity}
All messages broadcast by a correct process are eventually received by all non faulty processors. \\
Formally : \\
$\forall m, \forall p_i: \text{correct}(p_i) \wedge \text{bc-send}_i(m) => \forall p_j : \text{correct}(p_j) \Rightarrow \text{bc-recv}_j(m)$
\end{property}
\subsubsection{AtomicBroadcast Properties}
\begin{property}{AB Totally ordered}
$\forall m_1, m_2, \forall p_i, p_j : \text{ab-recv}_{p_i}(m_1) < \text{ab-recv}_{p_i}(m_2) \Rightarrow \text{ab-recv}_{p_j}(m_1) < \text{ab-recv}_{p_j}(m_2)$
\end{property}
\subsubsection{DenyList Properties}
Let $\Pi_M$ be the set of processes authorized to issue \texttt{APPEND} operations,
and $\Pi_V$ the set of processes authorized to issue \texttt{PROVE} operations. \\
Let $S$ be the set of valid values that may be appended. Let $\texttt{Seq}$ be
the linearization of operations recorded in the DenyList.
\begin{property}{APPEND Validity}
An operation $\texttt{APPEND}(x)$ is valid iff :
the issuing process $p \in \Pi_M$, and the value $x \in S$
\end{property}
\begin{property}{PROVE Validity}
An operation $\texttt{PROVE}(x)$ is valid iff:
the issuing process $p \in \Pi_V$, and there exists no $\texttt{APPEND}(x)$ that appears earlier in $\texttt{Seq}$.
\end{property}
\begin{property}{PROGRESS}
If an APPEND(x) is invoked by a correct process, then all correct processes will eventually be unable to PROVE(x).
\end{property}
\begin{property}{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{property}

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\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{csquotes}
\usepackage[french]{babel}
\usepackage[affil-it]{authblk}
\usepackage{fullpage}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{biblatex}
% \usepackage[linesnumbered,ruled,vlined]{algorithm2e}
\usepackage{algorithm}
\usepackage{algorithmicx}
\usepackage[noend]{algpseudocode}
\algrenewcommand\alglinenumber[1]{\tiny #1}
\usepackage{etoolbox}
% --- Partage du compteur de lignes entre plusieurs algorithmes
\makeatletter
\newcounter{algoLine}
\renewcommand{\alglinenumber}[1]{\arabic{algoLine}}
\newcommand{\nextalgline}{\stepcounter{algoLine}}
\newcommand{\resetalgline}{\setcounter{algoLine}{1}}
\makeatother
\newtheorem{property}{Property}
\newtheorem{theorem}{Theorem}
\newtheorem{proof}{Proof}
\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}
\subsection{proof}
\input{proof/index.tex}
\printbibliography
\end{document}

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\begin{theorem}[Integrity]
If a message $m$ is delivered by any process, then it was previously broadcast by some process via the \texttt{AB-broadcast} primitive.
\end{theorem}
\begin{proof}
Let $j$ be a process such that $\text{AB-deliver}_j(m)$ occurs.
\begin{align*}
&\text{AB-deliver}_j(m) & \text{(line 24)} \\
\Rightarrow\; &\exists r_0 : m \in \texttt{ordered}(M^{r_0}) & \text{(line 22)} \\
\Rightarrow\; &\exists j_0 : j_0 \in \textit{winner}^{r_0} \land m \in \textit{prop}[r_0][j_0] & \text{(line 21)} \\
\Rightarrow\; &\exists m_0, S_0 : \text{RB-received}_{j_0}(m_0, S_0, r_0, j_0) \land m \in S_0 & \text{(line 2)} \\
\Rightarrow\; &S_0 = (\textit{received}_{j_0} \setminus \textit{delivered}_{j_0}) \cup \{m_1\} & \text{(line 5)} \\
\Rightarrow\; &\textbf{if } m_1 = m: \exists\, \text{AB-broadcast}_{j_0}(m) \hspace{1em} \square \\
&\textbf{else if } m_1 \neq m: \\
&\quad m \in \textit{received}_{j_0} \setminus \textit{delivered}_{j_0} \Rightarrow m \in \textit{received}_{j_0} \land m \notin \textit{delivered}_{j_0} \\
&\quad \exists j_1, S_1, r_1 : \text{RB-received}_{j_1}(m, S_1, r_1, j_1) & \text{(line 1)} \\
&\quad \Rightarrow \exists\, \text{AB-broadcast}_{j_1}(m) \hspace{1em} \square & \text{(line 5)}
\end{align*}
\end{proof}
\begin{theorem}[No Duplication]
No message is delivered more than once by any process.
\end{theorem}
\begin{proof}
Let $j$ be a process such that both $\text{AB-deliver}_j(m_0)$ and $\text{AB-deliver}_j(m_1)$ occur, with $m_0 = m_1$.
\begin{align*}
&\text{AB-deliver}_j(m_0) \wedge \text{AB-deliver}_j(m_1) & \text{(line 24)} \\
\Rightarrow\; & m_0, m_1 \in \textit{delivered}_j & \text{(line 23)} \\
\Rightarrow\; &\exists r_0, r_1 : m_0 \in M^{r_0} \wedge m_1 \in M^{r_1} & \text{(line 22)} \\
\Rightarrow\; &\exists j_0, j_1 : m_0 \in \textit{prop}[r_0][j_0] \wedge m_1 \in \textit{prop}[r_1][j_1] \\
&\hspace{2.5em} \wedge\ j_0 \in \textit{winner}^{r_0},\ j_1 \in \textit{winner}^{r_1} & \text{(line 21)}
\end{align*}
We now distinguish two cases:
\vspace{0.5em}
\noindent\textbf{Case 1:} $r_0 = r_1$:
\begin{itemize}
\item If $j_0 \neq j_1$: this contradicts message uniqueness, since two different processes would include the same message in round $r_0$.
\item If $j_0 = j_1$:
\begin{align*}
\Rightarrow & |{(j_0, \texttt{PROVE}(r_0)) \in proves}| \geq 2 & \text{(line 19)}\\
\Rightarrow &\texttt{PROVE}_{j_0}(r_0) \text{ occurs 2 times} & \text{(line 6)}\\
\Rightarrow &\texttt{AB-Broadcast}_{j_0}(m_0) \text{ were invoked two times} \\
\Rightarrow &(max\{r: \exists j, (j, \texttt{PROVE}(r)) \in proves\} + 1) & \text{(line 4)}\\
&\text{ returned the same value in two differents invokations of \texttt{AB-Broadcast}} \\
&\textbf{But } \texttt{PROVE}(r_0) \Rightarrow \texttt{max}\{r: \exists j, (j, \texttt{PROVE}(r)) \in proves\} + 1 > r_0 \\
&\text{It's impossible for a single process to submit two messages in the same round} \hspace{1em} \\
\end{align*}
\end{itemize}
% \vspace{0.5em}
\noindent\textbf{Case 2:} $r_0 \ne r_1$:
\begin{itemize}
\item If $j_0 \neq j_1$: again, message uniqueness prohibits two different processes from broadcasting the same message in different rounds.
\item If $j_0 = j_1$: message uniqueness also prohibits the same process from broadcasting the same message in two different rounds.
\end{itemize}
In all cases, we reach a contradiction. Therefore, it is impossible for a process to deliver the same message more than once. $\square$
\end{proof}
% \subsubsection{No Duplication}
% $M = (\bigcup_{i \rightarrow |P|} AB\_receieved_{i}(m)), \not\exists m_0 m_1 \in M \text{s.t. } m_1 = m_2$
% \\
% Proof \\
% \begin{align*}
% &\text{Soit } i, m_0, m_1 \text{ tels que } m_0 = m_1 \\
% &\exists r_0,\ m_0 \in M^{r_0} \\
% &\exists r_1,\ m_1 \in M^{r_1} \\
% &\text{if } r_0 = r_1 \\
% &\quad \exists j_0, j_1,\ \text{prop tq } \text{prop}[r_0][j_0] = m_0,\ \text{prop}[r_0][j_1] = m_1 \quad j_0, j_1 \in \text{winnner}^{r_0} \\
% &\quad \text{if} j_0 \neq j_1 \\
% &\quad\quad \text{On admet qu'il est impossible pour un processus de soumettre le même msg qu'un autre} \\
% &\quad \text{if } j_0 = j_1 \\
% &\quad\quad j_0 \text{ a émis son } \text{PROVE}(r_0) \text{ valide 2 fois}\\
% &\quad\quad \text{Impossible si } j_0 \text{ correct} \\
% &\text{else} \\
% &\quad \exists j_0, j_1,\ \text{prop tq } \text{prop}[r_0][j_0] = m_0,\ \text{prop}[r_0][j_1] = m_1 \quad j_0, j_1 \in \text{winnner}^{r_0} \\
% &\quad \text{if } j_0 \neq j_1 \\
% &\quad\quad \text{On admet qu'il est impossible pour un processus de soumettre le même msg qu'un autre} \\
% &\quad \text{if } j_0 = j_1 \\
% &j_0 \text{ à emis et validé 2 fois le même messages a des rounds différents.}\\
% &\text{On admet que deux message identiques soumis a des rounds différents ne peuvent être identiques}
% \end{align*}
\subsubsection{Broadcast Validity}
$\exists j_0, m_0 \quad AB\_broadcast_{j_0}(m_0) \Rightarrow \forall j_1 \quad AB\_received_{j_1}(m_0)$ \\
Proof:
\begin{align*}
&\exists j_0, m_0 \quad AB\_broadcast_{j_0}(m_0) \\
&\forall j_1, \exists r_1 \quad RB\_deliver_{j_1}^{r_1}(m_0) \\
&\exists receieved : m_0 \in receieved_{j_1} \\
&\exists r_0 : RB\_deliver(PROP, r_0, m_0) & LOOP\\
&\exists prop: \text{prop}[r_0][j_0] = m_0 \\
&\text{if } \not\exists (j_0, PROVE(r_0)) \in \text{proves} \\
&\quad r_0 += 1 \\
&\quad \text{jump to LOOP} \\
&\text{else} \\
&\quad \exists \text{winner}, \text{winner}^{r_0} \ni j_0 \\
&\quad \exists M^{r_0} \ni (\text{prop}[r_0][j_0] = m_0) \\
&\quad \forall j_1, \quad AB\_deliver_{j_1}(m_0)
\end{align*}
\subsubsection*{AB receive width}
\[
\exists j_0, m_0 \quad AB\_deliver_{j_0}(m_0) \Rightarrow \forall j_1\ AB\_deliver_{j_1}
\]
Proof:
\begin{align*}
&\forall j_0, m_0\ AB\_deliver_{j_0}(m_0) \Rightarrow \exists j_1 \text{ correct }, AB\_broadcast(m_0) \\
&\exists j_0, m_0 \quad AB\_broadcast_{j_0}(m_0) \Rightarrow \forall j_1,\ AB\_deliver_{j_1}(m_0)
\end{align*}

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@article{saito_optimistic_2005,
title = {Optimistic {Replication}},
volume = {37},
url = {https://inria.hal.science/hal-01248208},
doi = {10.1145/1057977.1057980},
abstract = {Data replication is a key technology in distributed systems that enables higher availability and performance. This article surveys optimistic replication algorithms. They allow replica contents to diverge in the short term to support concurrent work practices and tolerate failures in low-quality communication links. The importance of such techniques is increasing as collaboration through wide-area and mobile networks becomes popular.Optimistic replication deploys algorithms not seen in traditional “pessimistic” systems. Instead of synchronous replica coordination, an optimistic algorithm propagates changes in the background, discovers conflicts after they happen, and reaches agreement on the final contents incrementally.We explore the solution space for optimistic replication algorithms. This article identifies key challenges facing optimistic replication systems---ordering operations, detecting and resolving conflicts, propagating changes efficiently, and bounding replica divergence---and provides a comprehensive survey of techniques developed for addressing these challenges.},
language = {en},
number = {1},
urldate = {2023-06-09},
journal = {ACM Computing Surveys},
author = {Saito, Yasushi and Shapiro, Marc},
year = {2005},
pages = {42},
file = {Saito et Shapiro - 2005 - Optimistic Replication.pdf:/home/amaury/Zotero/storage/4WJX5IAN/Saito et Shapiro - 2005 - Optimistic Replication.pdf:application/pdf},
}
@article{singh_zeno_2009,
title = {Zeno: {Eventually} {Consistent} {Byzantine}-{Fault} {Tolerance}},
abstract = {Many distributed services are hosted at large, shared, geographically diverse data centers, and they use replication to achieve high availability despite the unreachability of an entire data center. Recent events show that non-crash faults occur in these services and may lead to long outages. While Byzantine-Fault Tolerance (BFT) could be used to withstand these faults, current BFT protocols can become unavailable if a small fraction of their replicas are unreachable. This is because existing BFT protocols favor strong safety guarantees (consistency) over liveness (availability).},
language = {en},
author = {Singh, Atul and Fonseca, Pedro and Kuznetsov, Petr and Rodrigues, Rodrigo and Maniatis, Petros},
year = {2009},
file = {Singh et al. - Zeno Eventually Consistent Byzantine-Fault Tolera.pdf:/home/amaury/Zotero/storage/K6J2UEBK/Singh et al. - Zeno Eventually Consistent Byzantine-Fault Tolera.pdf:application/pdf},
}
@inproceedings{shakarami_refresh_2019,
title = {Refresh {Instead} of {Revoke} {Enhances} {Safety} and {Availability}: {A} {Formal} {Analysis}},
volume = {LNCS-11559},
shorttitle = {Refresh {Instead} of {Revoke} {Enhances} {Safety} and {Availability}},
url = {https://inria.hal.science/hal-02384596},
doi = {10.1007/978-3-030-22479-0_16},
abstract = {Due to inherent delays and performance costs, the decision point in a distributed multi-authority Attribute-Based Access Control (ABAC) system is exposed to the risk of relying on outdated attribute values and policy; which is the safety and consistency problem. This paper formally characterizes three increasingly strong levels of consistency to restrict this exposure. Notably, we recognize the concept of refreshing attribute values rather than simply checking the revocation status, as in traditional approaches. Refresh replaces an older value with a newer one, while revoke simply invalidates the old value. Our lowest consistency level starts from the highest level in prior revocation-based work by Lee and Winslett (LW). Our two higher levels utilize the concept of request time which is absent in LW. For each of our levels we formally show that using refresh instead of revocation provides added safety and availability.},
language = {en},
urldate = {2023-06-09},
publisher = {Springer International Publishing},
author = {Shakarami, Mehrnoosh and Sandhu, Ravi},
month = jul,
year = {2019},
pages = {301},
file = {Shakarami et Sandhu - 2019 - Refresh Instead of Revoke Enhances Safety and Avai.pdf:/home/amaury/Zotero/storage/XQNWKF7H/Shakarami et Sandhu - 2019 - Refresh Instead of Revoke Enhances Safety and Avai.pdf:application/pdf},
}
@article{misra_axioms_1986,
title = {Axioms for memory access in asynchronous hardware systems},
volume = {8},
issn = {0164-0925, 1558-4593},
url = {https://dl.acm.org/doi/10.1145/5001.5007},
doi = {10.1145/5001.5007},
abstract = {The problem of concurrent accesses to registers by asynchronous components is considered. A set of axioms about the values in a register during concurrent accesses is proposed. It is shown that if these axioms are met by a register, then concurrent accesses to it may be viewed as nonconcurrent, thus making it possible to analyze asynchronous algorithms without elaborate timing analysis of operations. These axioms are shown, in a certain sense, to be the weakest. Motivation for this work came from analyzing low-level hardware components in a VLSI chip which concurrently accesses a flip-flop.},
language = {en},
number = {1},
urldate = {2023-06-08},
journal = {ACM Transactions on Programming Languages and Systems},
author = {Misra, J.},
month = jan,
year = {1986},
pages = {142--153},
file = {Misra - 1986 - Axioms for memory access in asynchronous hardware .pdf:/home/amaury/Zotero/storage/KZP2774N/Misra - 1986 - Axioms for memory access in asynchronous hardware .pdf:application/pdf},
}
@article{lamport_interprocess_1986,
title = {On interprocess communication},
volume = {1},
issn = {1432-0452},
url = {https://doi.org/10.1007/BF01786228},
doi = {10.1007/BF01786228},
abstract = {Interprocess communication is studied without assuming any lower-level communication primitives. Three classes of communication registers are considered, and several constructions are given for implementing one class of register with a weaker class. The formalism developed in Part I is used in proving the correctness of these constructions.},
language = {en},
number = {2},
urldate = {2023-06-08},
journal = {Distributed Computing},
author = {Lamport, Leslie},
month = jun,
year = {1986},
keywords = {Communication Network, Computer Hardware, Computer System, Operating System, System Organization},
pages = {86--101},
file = {Lamport - 1986 - On interprocess communication.pdf:/home/amaury/Zotero/storage/XV7AEARN/Lamport - 1986 - On interprocess communication.pdf:application/pdf},
}
@book{lipton_pram_1988,
title = {{PRAM}: {A} {Scalable} {Shared} {Memory}},
shorttitle = {{PRAM}},
language = {en},
publisher = {Princeton University, Department of Computer Science},
author = {Lipton, Richard J. and Sandberg, Jonathan S.},
year = {1988},
note = {Google-Books-ID: 962epwAACAAJ},
file = {Lipton et Sandberg - 1988 - PRAM A Scalable Shared Memory.pdf:/home/amaury/Zotero/storage/3ZYT3WT4/Lipton et Sandberg - 1988 - PRAM A Scalable Shared Memory.pdf:application/pdf},
}
@inproceedings{hutto_slow_1990,
title = {Slow memory: weakening consistency to enhance concurrency in distributed shared memories},
shorttitle = {Slow memory},
url = {https://www.computer.org/csdl/proceedings-article/icdcs/1990/00089297/12OmNvSKNPr},
doi = {10.1109/ICDCS.1990.89297},
abstract = {The use of weakly consistent memories in distributed shared memory systems to combat unacceptable network delay and to allow such systems to scale is proposed. Proposed memory correctness conditions are surveyed, and how they are related by a weakness hierarchy is demonstrated. Multiversion and messaging interpretations of memory are introduced as means of systematically exploring the space of possible memories. Slow memory is presented as a memory that allows the effects of writes to propagate slowly through the system, eliminating the need for costly consistency maintenance protocols that limit concurrency. Slow memory processes a valuable locality property and supports a reduction from traditional atomic memory. Thus slow memory is as expressive as atomic memory. This expressiveness is demonstrated by two exclusion algorithms and a solution to M.J. Fischer and A. Michael's (1982) dictionary problem on slow memory.},
language = {English},
urldate = {2023-06-06},
publisher = {IEEE Computer Society},
author = {Hutto, P. W. and Ahamad, M.},
month = jan,
year = {1990},
pages = {302,303,304,305,306,307,308,309--302,303,304,305,306,307,308,309},
file = {Hutto et Ahamad - 1990 - Slow memory weakening consistency to enhance conc.pdf:/home/amaury/Téléchargements/Hutto et Ahamad - 1990 - Slow memory weakening consistency to enhance conc.pdf:application/pdf},
}
@article{lamport_how_1979,
title = {How to {Make} a {Multiprocessor} {Computer} {That} {Correctly} {Executes} {Multiprocess} {Programs}},
volume = {C-28},
issn = {1557-9956},
doi = {10.1109/TC.1979.1675439},
abstract = {Many large sequential computers execute operations in a different order than is specified by the program. A correct execution is achieved if the results produced are the same as would be produced by executing the program steps in order. For a multiprocessor computer, such a correct execution by each processor does not guarantee the correct execution of the entire program. Additional conditions are given which do guarantee that a computer correctly executes multiprocess programs.},
number = {9},
journal = {IEEE Transactions on Computers},
author = {{Lamport}},
month = sep,
year = {1979},
note = {Conference Name: IEEE Transactions on Computers},
keywords = {Computer design, concurrent computing, hardware correctness, multiprocessing, parallel processing},
pages = {690--691},
file = {IEEE Xplore Abstract Record:/home/amaury/Zotero/storage/IVGSSPNE/1675439.html:text/html;Lamport - 1979 - How to Make a Multiprocessor Computer That Correct.pdf:/home/amaury/Zotero/storage/GY8CWGUV/Lamport - 1979 - How to Make a Multiprocessor Computer That Correct.pdf:application/pdf},
}
@article{mosberger_memory_1993,
title = {Memory consistency models},
volume = {27},
issn = {0163-5980},
url = {https://dl.acm.org/doi/10.1145/160551.160553},
doi = {10.1145/160551.160553},
abstract = {This paper discusses memory consistency models and their influence on software in the context of parallel machines. In the first part we review previous work on memory consistency models. The second part discusses the issues that arise due to weakening memory consistency. We are especially interested in the influence that weakened consistency models have on language, compiler, and runtime system design. We conclude that tighter interaction between those parts and the memory system might improve performance considerably.},
language = {en},
number = {1},
urldate = {2023-06-06},
journal = {ACM SIGOPS Operating Systems Review},
author = {Mosberger, David},
month = jan,
year = {1993},
pages = {18--26},
file = {Mosberger - 1993 - Memory consistency models.pdf:/home/amaury/Zotero/storage/VF2ZNK6A/Mosberger - 1993 - Memory consistency models.pdf:application/pdf},
}
@incollection{goos_causal_1995,
address = {Berlin, Heidelberg},
title = {From causal consistency to sequential consistency in shared memory systems},
volume = {1026},
isbn = {978-3-540-60692-5 978-3-540-49263-4},
url = {http://link.springer.com/10.1007/3-540-60692-0_48},
language = {en},
urldate = {2023-06-06},
booktitle = {Foundations of {Software} {Technology} and {Theoretical} {Computer} {Science}},
publisher = {Springer Berlin Heidelberg},
author = {Raynal, Michel and Schiper, André},
editor = {Goos, Gerhard and Hartmanis, Juris and Leeuwen, Jan and Thiagarajan, P. S.},
year = {1995},
doi = {10.1007/3-540-60692-0_48},
note = {Series Title: Lecture Notes in Computer Science},
pages = {180--194},
file = {Raynal et Schiper - 1995 - From causal consistency to sequential consistency .pdf:/home/amaury/Zotero/storage/B8UNWUSA/Raynal et Schiper - 1995 - From causal consistency to sequential consistency .pdf:application/pdf},
}
@phdthesis{kumar_fault-tolerant_2019,
type = {{PhD} {Thesis}},
title = {Fault-{Tolerant} {Distributed} {Services} in {Message}-{Passing} {Systems}},
school = {Texas A\&M University},
author = {Kumar, Saptaparni},
year = {2019},
file = {Kumar - 2019 - Fault-Tolerant Distributed Services in Message-Pas.pdf:/home/amaury/Zotero/storage/Q9XK77W9/Kumar - 2019 - Fault-Tolerant Distributed Services in Message-Pas.pdf:application/pdf;Snapshot:/home/amaury/Zotero/storage/7JB26RAJ/1.html:text/html},
}
@article{somasekaram_high-availability_2022,
title = {High-{Availability} {Clusters}: {A} {Taxonomy}, {Survey}, and {Future} {Directions}},
volume = {187},
issn = {01641212},
shorttitle = {High-{Availability} {Clusters}},
url = {http://arxiv.org/abs/2109.15139},
doi = {10.1016/j.jss.2021.111208},
abstract = {The delivery of key services in domains ranging from finance and manufacturing to healthcare and transportation is underpinned by a rapidly growing number of mission-critical enterprise applications. Ensuring the continuity of these complex applications requires the use of software-managed infrastructures called high-availability clusters (HACs). HACs employ sophisticated techniques to monitor the health of key enterprise application layers and of the resources they use, and to seamlessly restart or relocate application components after failures. In this paper, we first describe the manifold uses of HACs to protect essential layers of a critical application and present the architecture of high availability clusters. We then propose a taxonomy that covers all key aspects of HACs -- deployment patterns, application areas, types of cluster, topology, cluster management, failure detection and recovery, consistency and integrity, and data synchronisation; and we use this taxonomy to provide a comprehensive survey of the end-to-end software solutions available for the HAC deployment of enterprise applications. Finally, we discuss the limitations and challenges of existing HAC solutions, and we identify opportunities for future research in the area.},
urldate = {2023-06-06},
journal = {Journal of Systems and Software},
author = {Somasekaram, Premathas and Calinescu, Radu and Buyya, Rajkumar},
month = may,
year = {2022},
note = {arXiv:2109.15139 [cs, eess]},
keywords = {Computer Science - Distributed, Parallel, and Cluster Computing, Computer Science - Networking and Internet Architecture, Electrical Engineering and Systems Science - Systems and Control},
pages = {111208},
file = {arXiv.org Snapshot:/home/amaury/Zotero/storage/B4KCP9BG/2109.html:text/html;Somasekaram et al. - 2022 - High-Availability Clusters A Taxonomy, Survey, an.pdf:/home/amaury/Zotero/storage/K3LQZLC8/Somasekaram et al. - 2022 - High-Availability Clusters A Taxonomy, Survey, an.pdf:application/pdf},
}
@book{perrin_concurrence_2017,
title = {Concurrence et cohérence dans les systèmes répartis},
isbn = {978-1-78405-295-9},
abstract = {La société moderne est de plus en plus dominée par la société virtuelle, le nombre d’internautes dans le monde ayant dépassé les trois milliards en 2015. A la différence de leurs homologues séquentiels, les systèmes répartis sont beaucoup plus difficiles à concevoir, et sont donc sujets à de nombreux problèmes.La cohérence séquentielle fournit la même vue globale à tous les utilisateurs, mais le confort d\&\#39;utilisation qu\&\#39;elle apporte est trop coûteux, voire impossible, à mettre en oeuvre à grande échelle. Concurrence et cohérence dans les systèmes répartis examine les meilleures façons de spécifier les objets que l’on peut tout de même implémenter dans ces systèmes.Cet ouvrage explore la zone grise des systèmes répartis et dresse une carte des critères de cohérence faible, identifiant plusieurs familles et démontrant comment elles peuvent s’intégrer dans un langage de programmation.},
language = {fr},
publisher = {ISTE Group},
author = {Perrin, Matthieu},
month = sep,
year = {2017},
note = {Google-Books-ID: 6DRlDwAAQBAJ},
file = {Perrin - 2017 - Concurrence et cohérence dans les systèmes réparti.pdf:/home/amaury/Téléchargements/Perrin - 2017 - Concurrence et cohérence dans les systèmes réparti.pdf:application/pdf},
}
@article{van_der_linde_practical_2020,
title = {Practical client-side replication: weak consistency semantics for insecure settings},
volume = {13},
issn = {2150-8097},
shorttitle = {Practical client-side replication},
url = {https://dl.acm.org/doi/10.14778/3407790.3407847},
doi = {10.14778/3407790.3407847},
abstract = {Client-side replication and direct client-to-client synchronization can be used to create highly available, low-latency interactive applications. Causal consistency, the strongest available consistency model under network partitions, is an attractive consistency model for these applications.},
language = {en},
number = {12},
urldate = {2023-06-06},
journal = {Proceedings of the VLDB Endowment},
author = {Van Der Linde, Albert and Leitão, João and Preguiça, Nuno},
month = aug,
year = {2020},
pages = {2590--2605},
file = {Van Der Linde et al. - 2020 - Practical client-side replication weak consistenc.pdf:/home/amaury/Zotero/storage/5TJ3SA56/Van Der Linde et al. - 2020 - Practical client-side replication weak consistenc.pdf:application/pdf},
}
@article{decandia_dynamo_2007,
title = {Dynamo: {Amazon}’s {Highly} {Available} {Key}-value {Store}},
abstract = {Reliability at massive scale is one of the biggest challenges we face at Amazon.com, one of the largest e-commerce operations in the world; even the slightest outage has significant financial consequences and impacts customer trust. The Amazon.com platform, which provides services for many web sites worldwide, is implemented on top of an infrastructure of tens of thousands of servers and network components located in many datacenters around the world. At this scale, small and large components fail continuously and the way persistent state is managed in the face of these failures drives the reliability and scalability of the software systems.},
language = {en},
author = {DeCandia, Giuseppe and Hastorun, Deniz and Jampani, Madan and Kakulapati, Gunavardhan and Lakshman, Avinash and Pilchin, Alex and Sivasubramanian, Swaminathan and Vosshall, Peter and Vogels, Werner},
year = {2007},
file = {DeCandia et al. - Dynamo Amazon’s Highly Available Key-value Store.pdf:/home/amaury/Zotero/storage/KDHRPBGR/DeCandia et al. - Dynamo Amazon’s Highly Available Key-value Store.pdf:application/pdf},
}
@misc{misra_byzantine_2021,
title = {Byzantine {Fault} {Tolerant} {Causal} {Ordering}},
url = {http://arxiv.org/abs/2112.11337},
abstract = {Causal ordering in an asynchronous system has many applications in distributed computing, including in replicated databases and real-time collaborative software. Previous work in the area focused on ordering point-to-point messages in a fault-free setting, and on ordering broadcasts under various fault models. To the best of our knowledge, Byzantine faulttolerant causal ordering has not been attempted for point-topoint communication in an asynchronous setting. In this paper, we first show that existing algorithms for causal ordering of point-to-point communication fail under Byzantine faults. We then prove that it is impossible to causally order messages under point-to-point communication in an asynchronous system with one or more Byzantine failures. We then present two algorithms that can causally order messages under Byzantine failures, where the network provides an upper bound on the message transmission time. The proofs of correctness for these algorithms show that it is possible to achieve causal ordering for point-to-point communication under a stronger asynchrony model where the network provides an upper bound on message transmission time. We also give extensions of our two algorithms for Byzantine fault-tolerant causal ordering of multicasts.},
language = {en},
urldate = {2023-07-12},
publisher = {arXiv},
author = {Misra, Anshuman and Kshemkalyani, Ajay},
month = dec,
year = {2021},
note = {arXiv:2112.11337 [cs]},
keywords = {Computer Science - Distributed, Parallel, and Cluster Computing},
file = {Misra and Kshemkalyani - 2021 - Byzantine Fault Tolerant Causal Ordering.pdf:/home/amaury/Zotero/storage/P2R366US/Misra and Kshemkalyani - 2021 - Byzantine Fault Tolerant Causal Ordering.pdf:application/pdf},
}
@inproceedings{tseng_distributed_2019,
title = {Distributed {Causal} {Memory} in the {Presence} of {Byzantine} {Servers}},
doi = {10.1109/NCA.2019.8935059},
abstract = {We study distributed causal shared memory (or distributed read/write objects) in the client-server model over asynchronous message-passing networks in which some servers may suffer Byzantine failures. Since Ahamad et al. proposed causal memory in 1994, there have been abundant research on causal storage. Lately, there is a renewed interest in enforcing causal consistency in large-scale distributed storage systems (e.g., COPS, Eiger, Bolt-on). However, to the best of our knowledge, the fault-tolerance aspect of causal memory is not well studied, especially on the tight resilience bound. In our prior work, we showed that 2 f+1 servers is the tight bound to emulate crash-tolerant causal shared memory when up to f servers may crash. In this paper, we adopt a typical model considered in many prior works on Byzantine-tolerant storage algorithms and quorum systems. In the system, up to f servers may suffer Byzantine failures and any number of clients may crash. We constructively present an emulation algorithm for Byzantine causal memory using 3 f+1 servers. We also prove that 3 f+1 is necessary for tolerating up to f Byzantine servers. In other words, we show that 3 f+1 is a tight bound. For evaluation, we implement our algorithm in Golang and compare their performance with two state-of-the-art fault-tolerant algorithms that ensure atomicity in the Google Cloud Platform.},
booktitle = {2019 {IEEE} 18th {International} {Symposium} on {Network} {Computing} and {Applications} ({NCA})},
author = {Tseng, Lewis and Wang, Zezhi and Zhao, Yajie and Pan, Haochen},
month = sep,
year = {2019},
note = {ISSN: 2643-7929},
keywords = {asynchrony, Byzantine faults, causal memory, Computer crashes, Consensus protocol, distributed storage system, Emulation, evaluation, Fault tolerance, Fault tolerant systems, History, Servers, tight condition},
pages = {1--8},
file = {IEEE Xplore Abstract Record:/home/amaury/Zotero/storage/DDV34ULW/8935059.html:text/html},
}

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# Enumération de la bibliographie étudié
## Cohérence
### Très pertinents
__perrin_concurrence_2017__, "Concurrence et cohérence dans les systèmes répartis":
Etat de l'art sur la cohérence dans les systèmes repartis. Présentation d'une approche de modélisation des histoires concurentes. Formaisations de différents critères de cohérences. Comparaison et "hierarchisation" des différents critères de cohérences.
### Intéressants mais redondants
__lamport_interprocess_1986__, "On interprocess communication":
Formalisation d'une cohérence séquentiel "single writer"
__misra_axioms_1986__, "Axioms for memory access in asynchronous hardware systems":
Exetnsion de lamport_interprocess_1986 dans une approche "multi-writer"
__lipton_pram_1988__, "{PRAM}: A Scalable Shared Memory":
Definition de la mémoire PRAM (cohérence pipeline).
## Cohérence en contextes byzantins
### Algorithmes
__van_der_linde_practical_2020__, "Practical client-side replication: weak consistency semantics for insecure settings":
Algorithme pour de la Cohérence causale BFT. (Reflexions sur des erreurs byzantines possible + algo et implé)
__kumar_fault-tolerant_2019__, "Fault-Tolerant Distributed Services in Message-Passing Systems":
Pas spécifiquement à propos des fautes byzantines dans la cohérence faible mais fait un panorama des differentes fautes non-byzantine possibles dans les systèmes distribués.
__singh_zeno_2009__, "Zeno: Eventually Consistent Byzantine-Fault Tolerance":
Algorithme pour de la convergence BFT. (Reflexions sur des erreurs byzanties possible + algo et implé)
__tseng_distributed_2019__, "Algo BFT pour cohérence causale (preuve + experiences)"
__misra_byzantine_2021__, "Preuve d'impossibilité de BFT dans un certain contexte pour de la cohérence causale + 2 algo pour de la cohérence causale BFT"4
## YJS
articles
- blog post: <https://blog.kevinjahns.de/are-crdts-suitable-for-shared-editing/>
- A string-wise CRDT algorithm for smart and large-scale collaborative editing systems <https://www.sciencedirect.com/science/article/abs/pii/S1474034616301811>
- Near Real-Time Peer-to-Peer Shared Editing on Extensible Data Types
## Complexity and specification of collaborative text editing
- Specification and space complexity of collaborative text editing Attiya et. all PODC/TCS
- Replicated data types: specification, verification, optimality Gosman et. al POPL (2014)

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# Articles à traiter
- [x] Tame the Wild with Byzantine Linearizability (DISC 2021)
- [ ] Atomic Register Abstractions for Byzantine-Prone
Distributed Systems, Extended Version
<https://hal.science/hal-04213718/document>
- [ ] <https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-207.pdf?TB_iframe=true&width=370.8&height=658.8>
- [ ] [https://www.sciencedirect.com/science/article/abs/pii/S0167404821002601](https://www.sciencedirect.com/science/article/abs/pii/S0167404821002601/)
- [ ] @ARTICLE{9585170,
  author={Shore, Malcolm and Zeadally, Sherali and Keshariya, Astha},
  journal={Computer},
  title={Zero Trust: The What, How, Why, and When},
  year={2021},
  volume={54},
  number={11},
  pages={26-35},
  doi={10.1109/MC.2021.3090018}}
- [ ] @ARTICLE{9773102,
  author={Syed, Naeem Firdous and Shah, Syed W. and Shaghaghi, Arash and Anwar, Adnan and Baig, Zubair and Doss, Robin},
  journal={IEEE Access},
  title={Zero Trust Architecture (ZTA): A Comprehensive Survey},
  year={2022},
  volume={10},
  number={},
  pages={57143-57179},
  doi={10.1109/ACCESS.2022.3174679}}