From 35a9d91779f949fa6f61a890721ffbd8704c980c Mon Sep 17 00:00:00 2001 From: Amaury JOLY Date: Fri, 27 Jun 2025 07:53:09 +0000 Subject: [PATCH] encore pas bon --- Recherche/ALDLoverAB/algo/index.tex | 59 +++++++---- Recherche/ALDLoverAB/main.pdf | Bin 303816 -> 280529 bytes Recherche/ALDLoverAB/proof/index.tex | 141 ++++++++++++++------------- 3 files changed, 110 insertions(+), 90 deletions(-) diff --git a/Recherche/ALDLoverAB/algo/index.tex b/Recherche/ALDLoverAB/algo/index.tex index b7e5fc2..a17bc48 100644 --- a/Recherche/ALDLoverAB/algo/index.tex +++ b/Recherche/ALDLoverAB/algo/index.tex @@ -5,19 +5,22 @@ We consider a set of processes communicating asynchronously over reliable point- \item \textbf{\textit{delivered}}: the set of messages that have been ordered. \item \textbf{\textit{prop}[$r$][$j$]}: the proposal set announced by process $j$ at round $r$. It contains a set of messages that process $j$ claims to have received but not yet delivered. \item \textbf{\textit{winner}$^r$}: the set of processes that have issued a valid \texttt{PROVE} for round $r$, as observed through the registry. + \item \textbf{\textit{window}}: the list of the ids from the $f+1$ last rounds. \textit{window.pop()} remove the first value of the array. \textit{window.push(x)} append x as the last value of the array. \item \textbf{\texttt{RB-cast}$(\texttt{PROP}, S, r, j)$}: a reliable broadcast invocation that disseminates the proposal $S$ from process $j$ for round $r$. \item \textbf{\texttt{RB-delivered}$(\texttt{PROP}, S, r, j)$}: the handler invoked upon reception of a \texttt{RB-cast}, which stores the received proposal $S$ into $\textit{prop}[r][j]$. \item \textbf{\texttt{READ}()} : returns the current view of all valid operations stored in the DenyList registry. \item \textbf{\texttt{ordered}$(S)$}: returns a deterministic total order over a set $S$ of messages. + \item \textbf{\texttt{hash}$(T, r)$}: returns the identifier of the next round as a deterministic function of the delivered set $T$ and current round $r$. \end{itemize} \resetalgline \begin{algorithm} \caption{Atomic Broadcast with DenyList} - \begin{algorithmic}[1] + \begin{algorithmic}[1] \State $\textit{proves} \gets \emptyset$ \State $\textit{received} \gets \emptyset$ \State $\textit{delivered} \gets \emptyset$ + \State $\textit{window} \gets [\bot]^{f+1}$ \State $r_1 \gets 0$ \vspace{1em} @@ -29,31 +32,47 @@ We consider a set of processes communicating asynchronously over reliable point- % --- RB-delivered --- \State \nextalgline \textbf{RB-delivered}$_j(m)$ \State \nextalgline \hspace{1em} $\textit{received} \gets \textit{received} \cup \{m\}$ - \State \nextalgline \hspace{1em} \textbf{repeat until} $\textit{received} \setminus \textit{delivered} \neq \emptyset$ + \State \nextalgline \hspace{1em} \textbf{repeat while} $\textit{received} \setminus \textit{delivered} \neq \emptyset$ \State \nextalgline \hspace{2em} $S \gets \textit{received} \setminus \textit{delivered}$ + \State \nextalgline \hspace{2em} $\texttt{RB-broadcast}(\texttt{PROP}, S, r_1, j)$ \State \nextalgline \hspace{2em} $\textit{proves} \gets \texttt{READ}()$ - \State \nextalgline \hspace{2em} $r_2 \gets \max\{r : j,\ (j, \texttt{PROVE}(r)) \in \textit{proves}\} + 1$ - \State \nextalgline \hspace{2em} $\texttt{RB-cast}(\texttt{PROP}, S, r_2, j)$ - \State \nextalgline \hspace{2em} $\texttt{PROVE}(r_2)$ + \State \nextalgline \hspace{2em} $\texttt{PROVE}[j](r_1)$ + % \State \nextalgline \hspace{2em} $r_1 \gets \max\{r : j,\ (j, \texttt{PROVE}(r)) \in \textit{proves}\} + 1$ + + \vspace{0.5em} + \State \nextalgline \hspace{2em} $\texttt{APPEND}[j](r_1)$ + \State \nextalgline \hspace{2em} $S \gets \{1, ..., n\}$ + \State \nextalgline \hspace{2em} \textbf{repeat while} $|S| \leq n - f$ + \State \nextalgline \hspace{3em} \textbf{forall} $i \in S$ + \State \nextalgline \hspace{4em} \textbf{if} $\neg \texttt{PROVE}[i](r_1)$ + \State \nextalgline \hspace{5em} $S \gets S \setminus i$ \vspace{0.5em} - \State \nextalgline \hspace{2em} \textbf{for } $r \in [r_1 + 1, \dots, r_2]$ \textbf{do} - \State \nextalgline \hspace{3em} $\texttt{APPEND}(r)$ - \State \nextalgline \hspace{3em} $\textit{proves} \gets \texttt{READ}()$ - \State \nextalgline \hspace{3em} $\textit{winner}^r \gets \{j : (j, \texttt{PROVE}(r)) \in \textit{proves}\}$ - \State \nextalgline \hspace{3em} \textbf{wait } $\forall j \in \textit{winner}^r,\ \textit{prop}[r][j] \neq \bot$ - \State \nextalgline \hspace{3em} $T \gets \bigcup_{j \in \textit{winner}^r} \textit{prop}[r][j] \setminus \textit{delivered}$ + \State \nextalgline \hspace{2em} $\textit{winner}[r_1] \gets \texttt{READ\_ALL}()$ + \State \nextalgline \hspace{2em} \textbf{wait } $\forall j \in \textit{winner}[r_1],\ |\textit{prop}[r_1][j] \neq \bot| \geq f+1$ + \State \nextalgline \hspace{2em} $T \gets \bigcup_{j \in \textit{winner}[r_1]} \textit{prop}[r_1][j] \setminus \textit{delivered}$ \vspace{0.5em} - \State \nextalgline \hspace{3em} \textbf{for each } $m \in \texttt{ordered}(T)$ - \State \nextalgline \hspace{4em} $\textit{delivered} \gets \textit{delivered} \cup \{m\}$ - \State \nextalgline \hspace{4em} $\texttt{AB-deliver}_j(m)$ - \State \nextalgline \hspace{2em} $r_1 \gets r_2$ + \State \nextalgline \hspace{2em} \textbf{for each } $m \in \texttt{ordered}(T)$ + \State \nextalgline \hspace{3em} $\textit{delivered} \gets \textit{delivered} \cup \{m\}$ + \State \nextalgline \hspace{3em} $\texttt{AB-deliver}_j(m)$ + \State \nextalgline \hspace{2em} $r_1 \gets \textit{hash}(T, r_1)$ \vspace{1em} - % --- RB-deliver(Prop) handler --- - \State \nextalgline \textbf{RB-delivered}$_j(\texttt{PROP}, S, r_1, j_1)$ - \State \nextalgline \hspace{1em} $\textit{prop}[r_1][j_1] \gets S$ + % --- READ_ALL() --- + \State \nextalgline \textbf{READ\_ALL}$(r)$ + \State \nextalgline \hspace{1em} \textbf{for each } $j \in (1, ... , n)$ + \State \nextalgline \hspace{2em} $win[j] \gets \{j_1: \texttt{READ}_{j_1}() \ni (j, \texttt{PROVE}(r))\}$ + \State \nextalgline \hspace{1em} \textbf{for} $i \in (1, ... , n)$ + \State \nextalgline \hspace{2em} \textbf{for} $j \in (1, ... , n)$ + \State \nextalgline \hspace{3em} \textbf{if} $i \in win[j]$ + \State \nextalgline \hspace{4em} $count[i] ++$ + \State \nextalgline \hspace{1em} \textbf{return} $\{i: count[i] \geq n-f\}$ - \end{algorithmic} -\end{algorithm} \ No newline at end of file + \end{algorithmic} +\end{algorithm} + +\subsection{Round mecansism} + +We assume that the hash function is deterministic and without collisions. 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