typo et quelques lemmes

Recherche/BFT-ARBover/2_Primitives/index.tex

@@ -2,14 +2,14 @@
 
 \RB provides the following properties in the model.
 \begin{itemize}[leftmargin=*]
-  \item \textbf{Integrity}: Every message received was previously sent. $\forall p_i:\ \RBreceived_i(m) \Rightarrow \exists p_j:\ \RBcast_j(m)$.
+  \item \textbf{Integrity}: Every message received was previously sent. $\forall p_i:\ m = \RBreceived_i() \Rightarrow \exists p_j:\ \RBcast_j(m)$.
   \item \textbf{No-duplicates}: No message is received more than once at any process.
   \item \textbf{Validity}: If a correct process broadcasts $m$, every correct process eventually receives $m$.
 \end{itemize}
 
 \subsection{DenyList Object}
 
- We assume a synchronous DenyList (\DL) object as in~\cite{frey:disc23} with the following properties.
+ We assume a linearizable DenyList (\DL) object as in~\cite{frey:disc23} with the following properties.
   
     The DenyList object type supports three operations: $\APPEND$, $\PROVE$, and $\READ$. These operations appear as if executed in a sequence $\Seq$ such that:
     \begin{itemize}
@@ -17,18 +17,18 @@
       \item \textbf{APPEND Validity.} The invocation of $\APPEND(x)$ by a process $p$ is valid if:
       \begin{itemize}
         \item $p \in \Pi_M \subseteq \Pi$; \textbf{and}
-        \item $x \in S$, where $S$ is a predefined set. 
+        \item $x \in S$, where $S$ denote the universe of valid entries to be appended to the DenyList.
       \end{itemize} 
       Otherwise, the operation is invalid.
-      \item \textbf{PROVE Validity.} If the invocation of a $op = \PROVE(x)$ by a correct process $p$ is not valid, then:  
+      \item \textbf{PROVE Validity.} Let $op$ the invocation of $\PROVE(x)$ by a process $p_i$. We said $op$ to be invalid, if and only if:  
       \begin{itemize}
         \item $p \not\in \Pi_V \subseteq \Pi$; \textbf{or}
         \item A valid $\APPEND(x)$ appears before $op$ in $\Seq$. 
       \end{itemize}
-      Otherwise, the operation is valid.
+      Otherwise, the operation is said to be valid.
       \item \textbf{PROVE Anti-Flickering.} If the invocation of a operation $op = \PROVE(x)$ by a correct process $p \in \Pi_V$ is invalid, then any $\PROVE(x)$ operation that appears after $op$ in $\Seq$ is invalid.
       \item \textbf{READ Validity.} The invocation of $op = \READ()$ by a process $p \in \pi_V$ returns the list of valid invocations of $\PROVE$ that appears before $op$ in $\Seq$ along with the names of the processes that invoked each operation. 
-      item \textbf{Anonymity.} Let us assume the process $p$ invokes a $\PROVE(v)$ operation. If the process $p'$ invokes a $\READ()$ operation, then $p'$ cannot learn the value $v$ unless $p$ leaks additional information.
+      % \item \textbf{Anonymity.} Let us assume the process $p$ invokes a $\PROVE(v)$ operation. If the process $p'$ invokes a $\READ()$ operation, then $p'$ cannot learn the value $v$ unless $p$ leaks additional information.
     \end{itemize}
   
-    We assume that $\Pi_M = \Pi_V = \Pi$ (all processes can invoke \APPEND and \PROVE).
+    We assume that $\Pi_M = \Pi_V = \Pi$ (all processes can invoke $\APPEND$ and $\PROVE$).