diff --git a/Recherche/AllowListDenyList/algo/index.tex b/Recherche/AllowListDenyList/algo/index.tex deleted file mode 100644 index 09372ac..0000000 --- a/Recherche/AllowListDenyList/algo/index.tex +++ /dev/null @@ -1,60 +0,0 @@ -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} \ No newline at end of file diff --git a/Recherche/AllowListDenyList/intro/index.tex b/Recherche/AllowListDenyList/intro/index.tex deleted file mode 100644 index 2064575..0000000 --- a/Recherche/AllowListDenyList/intro/index.tex +++ /dev/null @@ -1,77 +0,0 @@ - -\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 $f \forall p_j : \text{correct}(p_j) \Rightarrow \text{bc-recv}_j(m)$ -\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} \ No newline at end of file diff --git a/Recherche/AllowListDenyList/main.aux b/Recherche/AllowListDenyList/main.aux deleted file mode 100644 index 1051343..0000000 --- a/Recherche/AllowListDenyList/main.aux +++ /dev/null @@ -1,20 +0,0 @@ -\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}Algo}{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/Recherche/AllowListDenyList/main.bbl b/Recherche/AllowListDenyList/main.bbl deleted file mode 100644 index 1b062e4..0000000 --- a/Recherche/AllowListDenyList/main.bbl +++ /dev/null @@ -1,20 +0,0 @@ -% $ 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. 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diff --git a/Recherche/AllowListDenyList/main.pdf b/Recherche/AllowListDenyList/main.pdf deleted file mode 100644 index e379b85..0000000 Binary files a/Recherche/AllowListDenyList/main.pdf and /dev/null differ diff --git a/Recherche/AllowListDenyList/main.synctex.gz b/Recherche/AllowListDenyList/main.synctex.gz deleted file mode 100644 index b2df797..0000000 Binary files a/Recherche/AllowListDenyList/main.synctex.gz and /dev/null differ diff --git a/Recherche/AllowListDenyList/main.tex b/Recherche/AllowListDenyList/main.tex deleted file mode 100644 index d8ca704..0000000 --- a/Recherche/AllowListDenyList/main.tex +++ /dev/null @@ -1,63 +0,0 @@ -\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} \ No newline at end of file diff --git a/Recherche/AllowListDenyList/proof/index.tex b/Recherche/AllowListDenyList/proof/index.tex deleted file mode 100644 index a41d896..0000000 --- a/Recherche/AllowListDenyList/proof/index.tex +++ /dev/null @@ -1,121 +0,0 @@ -\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*} \ No newline at end of file diff --git a/Recherche/AllowListDenyList/sources.bib b/Recherche/AllowListDenyList/sources.bib deleted file mode 100644 index e69de29..0000000