reformatage

Recherche/BFT-ARBover/3_GEO_CS/index.tex

@@ -34,18 +34,26 @@
     DenyList as follows.
     
     \begin{algorithmic}
-      \Function{CANDIDATE}{$r$}
+      \begin{algorithm}[H]
-        \State $\PROVE(r)$
+        \caption{Group Election implementation using DenyList}
-      \EndFunction
+
-      \vspace{1em}
+        \Function{CANDIDATE}{$r$}
-      \Function{CLOSE}{$r$}
+          \State $\PROVE(r)$
-        \State $\APPEND(r)$
+        \EndFunction
-      \EndFunction
+        
-      \vspace{1em}
+        \vspace{1em}
-      \Function{READGE}{$r$}
+        
-        \State $P \gets \READ()$
+        \Function{CLOSE}{$r$}
-        \State \Return $\{ j : (j,\PROVEtrace(r)) \in P \}$
+          \State $\APPEND(r)$
-      \EndFunction
+        \EndFunction
+        
+        \vspace{1em}
+        
+        \Function{READGE}{$r$}
+          \State $P \gets \READ()$
+          \State \Return $\{ j : (j,\PROVEtrace(r)) \in P \}$
+        \EndFunction
+      \end{algorithm}
     \end{algorithmic}
     
     \paragraph{Termination.} Termination follows from the Termination property of DenyList operations. Consider now a fixed sequential history $\mathsf{Seq}$ of the DenyList.
@@ -71,26 +79,29 @@
     
     The operations are implemented as follows.
       
-    \begin{algorithmic}
+    \begin{algorithm}[H]
-      \Function{APPEND}{$r$}
+      \begin{algorithmic}
-        \State $\CLOSE(r)$
+        \caption{Group Election implementation using DenyList}
-      \EndFunction
+        \Function{APPEND}{$r$}
-      \vspace{1em}
+          \State $\CLOSE(r)$
-      \Function{PROVE}{$r$}
+        \EndFunction
-        \State $\CANDIDATE(r)$
+        \vspace{1em}
-        \State $W_r \gets \READGE(r)$
+        \Function{PROVE}{$r$}
-        \If{$p \in W_r$}
+          \State $\CANDIDATE(r)$
-          \State \Return \texttt{True}
+          \State $W_r \gets \READGE(r)$
-        \Else
+          \If{$p \in W_r$}
-          \State \Return \texttt{False}
+            \State \Return \texttt{True}
-        \EndIf
+          \Else
-      \EndFunction
+            \State \Return \texttt{False}
-      \vspace{1em}
+          \EndIf
-      \Function{READ}{$ $}
+        \EndFunction
-        \State $W \gets \bigcup_{\forall r \in S}\READGE(r)$
+        \vspace{1em}
-        \State \Return $\{(p,r) \mid p \in W_r\}$
+        \Function{READ}{$ $}
-      \EndFunction
+          \State $W \gets \bigcup_{\forall r \in S}\READGE(r)$
-    \end{algorithmic}
+          \State \Return $\{(p,r) \mid p \in W_r\}$
+        \EndFunction
+      \end{algorithmic}
+    \end{algorithm}
   
     \paragraph{Termination.} Termination follows from the Termination property of Group Election operations. Consider now a fixed sequential history $\mathsf{Seq}$ of the Group Election.