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ADoverAB v2

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Amaury JOLY
2025-05-02 07:22:19 +00:00
parent aefa847e9b
commit 23b4126f7e
5 changed files with 78 additions and 23 deletions
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79
recherches/ALDLoverAB/algo/index.tex
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@ -1,14 +1,43 @@
We define $k$ as the id of the round \\
the $getMax(..)$ function able to return the highest round played in the system.
the $getMax(proves)$ return $MAX({(\_, r) : \exists (\_, PROVE(r)) \in proves})$ \\
$buffer$ a FIFO list with $buffer[front]$ returning the first element
% \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}
\begin{algorithm}[H]
\DontPrintSemicolon
\SetAlgoLined
\KwIn{le message $m$}
\BlankLine
k\_max = getMax(READ()) \\
\While{buffer $\neq [\emptyset] $}{
(i, m) = buffer[front] \\
\textbf{wait} PROVE(k\_max || m) = false \\
proves = READ() \\
\If{$((i, PROVE(k\_max || m)) \in proves) \wedge ((i, PROVE(k\_max)) \in proves)$}{
$buffer = buffer - \{(i, m)\}$
}
}
\BlankLine
\While{true}{
proves = READ() \\
k = getMax(dump) + 1 \\
k = getMax(proves) + 1 \\
PROVE(k || m) \\
APPEND(k || m) \\
\If{PROVE(k)}{
APPEND(k) \\
@ -18,29 +47,55 @@ the $getMax(..)$ function able to return the highest round played in the system.
\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 \\
$proves_r = {(i, r) : \forall i, \exists (i, PROVE(r)) \in proves}$ \\
$proves_r^i = ((i, r) : \exists (i, PROVE(r)) \in proves)$ ?? NULL \\
% $proves_r \subseteq proves$ 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
buffer = $[\emptyset]$ \\
k = 0 \\
\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. $PROVE(r || m) \in proves$)
\If{$(\exists m : \exists(i, PROVE(r || m)) \in proves)$}{
\uIf{$(\exists(i, PROVE(r)) \in proves)$} {
AB\_Recv(m)
}
\Else{
$buffer = buffer \cup \{(i, m)\}$
}
}
}
}
}
\caption{AB\_Listen}
\end{algorithm}
\caption{AB\_Listen}
\end{algorithm}
% \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}