101 lines
2.4 KiB
TeX
101 lines
2.4 KiB
TeX
We define $k$ as the id of the round \\
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the $getMax(proves)$ return $MAX({(\_, r) : \exists (\_, PROVE(r)) \in proves})$ \\
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$buffer$ a FIFO list with $buffer[front]$ returning the first element
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% \begin{algorithm}[H]
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% \DontPrintSemicolon
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% \SetAlgoLined
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% \KwIn{le message $m$}
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% \BlankLine
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% \While{true}{
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% proves = READ() \\
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% k = getMax(dump) + 1 \\
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% APPEND(k || m) \\
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% \If{PROVE(k)}{
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% APPEND(k) \\
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% return
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% }
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% }
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% \caption{AB\_Broadcast}
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% \end{algorithm}
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\begin{algorithm}[H]
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\DontPrintSemicolon
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\SetAlgoLined
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\KwIn{le message $m$}
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\BlankLine
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k\_max = getMax(READ()) \\
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\While{buffer $\neq [\emptyset] $}{
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(i, m) = buffer[front] \\
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\textbf{wait} PROVE(k\_max || m) = false \\
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proves = READ() \\
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\If{$((i, PROVE(k\_max || m)) \in proves) \wedge ((i, PROVE(k\_max)) \in proves)$}{
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$buffer = buffer - \{(i, m)\}$
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}
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}
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\BlankLine
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\While{true}{
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proves = READ() \\
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k = getMax(proves) + 1 \\
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PROVE(k || m) \\
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APPEND(k || m) \\
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\If{PROVE(k)}{
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APPEND(k) \\
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return
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}
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}
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\caption{AB\_Broadcast}
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\end{algorithm}
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$proves_r = {(i, r) : \forall i, \exists (i, PROVE(r)) \in proves}$ \\
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$proves_r^i = ((i, r) : \exists (i, PROVE(r)) \in proves)$ ?? NULL \\
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% $proves_r \subseteq proves$ s.a. $\forall PROVE(x) \in proves_r$, x is in the form $r || m$ with $m$ who cannot be empty \\
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% $proves_r^i$ is the $PROVE(r || m )$ operation submited by the process i if exist \\
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\begin{algorithm}[H]
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\DontPrintSemicolon
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\SetAlgoLined
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buffer = $[\emptyset]$ \\
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k = 0 \\
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\BlankLine
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\While{true}{
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proves = READ() \\
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k\_max = getMax(proves) \\
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\For{r=k+1 \emph{\KwTo} k\_max}{
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APPEND(r)\\
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\For{i = 1 \emph{\KwTo} $|P|$}{
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\If{$(\exists m : \exists(i, PROVE(r || m)) \in proves)$}{
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\uIf{$(\exists(i, PROVE(r)) \in proves)$} {
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AB\_Recv(m)
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}
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\Else{
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$buffer = buffer \cup \{(i, m)\}$
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}
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}
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}
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}
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}
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\caption{AB\_Listen}
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\end{algorithm}
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% \begin{algorithm}[H]
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% \DontPrintSemicolon
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% \SetAlgoLined
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% \BlankLine
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% \While{true}{
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% proves = READ() \\
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% k\_max = getMax(proves) \\
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% \For{r=k+1 \emph{\KwTo} k\_max}{
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% APPEND(r)\\
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% $proves_r$ = \{$\forall i, PROVE(r)_i \in READ()$\} \\
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% \For{i = 1 \emph{\KwTo} $|P|$}{
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% \If{$\exists PROVE(r)_i \in proves_r$}{
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% AB\_Recv($m$ s.t. $PROVE(r || m) \in proves$)
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% }
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% }
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% }
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% }
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% \caption{AB\_Listen}
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% \end{algorithm} |