ALDoverABv1

recherches/ALDLoverAB/algo/index.tex

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+We define $k$ as the id of the round \\
+the $getMax(..)$ function able to return the highest round played in the system. 
+
+\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}
+
+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 \\
+
+\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}