ALDoverABv1

recherches/ALDLoverAB/intro/index.tex

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+
+\subsubsection{Model Properties}
+
+The model is defined as Message-passing Aysnchronous. \\
+There is n process. Each process is associated to a unique unforgeable id $i$.\\
+Each process know the identity of all the process in the system\\
+Each process have a reliable communication channel with all the others process such as:
+\begin{itemize}
+  \item send(m) is the send primitive
+  \item recv(m) is the reception primitive
+\end{itemize}
+A message send is eventualy received\\
+The system is Crash-Prone. There is at most f process who can crash such as f < n.\\
+
+
+\subsubsection{AtomicBroadcast Properties}
+
+\begin{theorem}{AB\_broadcast Validity}
+  if a message is sent by a correct process, the message is eventually received by all the correct process. 
+\end{theorem}
+
+\begin{theorem}{AB\_receive Validity}
+  if a message is received by a correct process, the message is eventually received by all the correct process. 
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety No creation}
+  if a message is received by a correct process, the message was emitted by a correct porcess. 
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety No duplication}
+  each message is received at most 1 time by each process. 
+\end{theorem}
+
+\begin{theorem}{AB\_receive safety Ordering}
+  $\forall m_1, m_2$ two messages, $\forall p_i, p_j$ two process. \\
+  if AB\_recv(m1) and AB\_recv(m2) for $p_i, p_j$ \\
+  and AB\_recv(m1) is before AB\_recv(m2) for $p_i$ \\
+  so AB\_recv(m1) is before AB\_recv(m2) for $p_j$ \\
+\end{theorem}
+
+
+
+\subsubsection{DenyList Properties}
+
+\begin{theorem}{APPEND Validity}
+  a APPEND(x) is valid iff the process p who sent the operation is such as $p \in \Pi_M$.
+  And iff $x \in S$ where S is a set of valid values.
+\end{theorem}
+
+\begin{theorem}{PROVE Validity}
+  a PROVE(x) is valid iff the process $p$ who sent the operation is such as $p \in \Pi_V$.
+  And iff $\exists$ APPEND(x) who appears before PROVE(x) in Seq.
+\end{theorem}
+
+\begin{theorem}{PROGRESS}
+  if an APPEND(x) is invoked, so there is a point in the linearization of the operations such as all PROVE(x) are valids.
+\end{theorem}
+
+\begin{theorem}{READ Validity}
+  READ() return a list of tuples who is a random permutation of all valids PROVE() associated to the identity of the emiter process. 
+\end{theorem}