From 01f1e546d4cfa8441c55edfe13a42120b80d9346 Mon Sep 17 00:00:00 2001 From: Amaury JOLY Date: Wed, 30 Apr 2025 07:07:35 +0000 Subject: [PATCH] ALDoverABv1 --- recherches/ALDLoverAB/ABAL.pdf | Bin 0 -> 204128 bytes recherches/ALDLoverAB/algo/index.tex | 46 + recherches/ALDLoverAB/intro/index.tex | 61 + recherches/ALDLoverAB/main.aux | 20 + recherches/ALDLoverAB/main.bbl | 20 + recherches/ALDLoverAB/main.bbl-SAVE-ERROR | 20 + recherches/ALDLoverAB/main.bcf | 2416 +++++++++++++++++++++ recherches/ALDLoverAB/main.fdb_latexmk | 97 + recherches/ALDLoverAB/main.fls | 153 ++ recherches/ALDLoverAB/main.log | 496 +++++ recherches/ALDLoverAB/main.pdf | Bin 0 -> 204949 bytes recherches/ALDLoverAB/main.run.xml | 85 + recherches/ALDLoverAB/main.synctex.gz | Bin 0 -> 13547 bytes recherches/ALDLoverAB/main.tex | 41 + recherches/ALDLoverAB/sources.bib | 0 15 files changed, 3455 insertions(+) create mode 100644 recherches/ALDLoverAB/ABAL.pdf create mode 100644 recherches/ALDLoverAB/algo/index.tex 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+\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} \ No newline at end of file diff --git a/recherches/ALDLoverAB/intro/index.tex b/recherches/ALDLoverAB/intro/index.tex new file mode 100644 index 0000000..81a78a7 --- /dev/null +++ b/recherches/ALDLoverAB/intro/index.tex @@ -0,0 +1,61 @@ + +\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} \ No newline at end of file diff --git a/recherches/ALDLoverAB/main.aux b/recherches/ALDLoverAB/main.aux new file mode 100644 index 0000000..8a52018 --- /dev/null +++ b/recherches/ALDLoverAB/main.aux @@ -0,0 +1,20 @@ +\relax +\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo } +\@nameuse{bbl@beforestart} +\catcode `:\active +\catcode `;\active +\catcode `!\active +\catcode `?\active +\abx@aux@refcontext{nty/global//global/global/global} +\providecommand \oddpage@label [2]{} +\babel@aux{french}{} +\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Model}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Model Properties}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}AtomicBroadcast Properties}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.3}DenyList Properties}{1}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Algorithms}{1}{}\protected@file@percent } +\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces AB\_Broadcast}}{2}{}\protected@file@percent } +\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces AB\_Listen}}{2}{}\protected@file@percent } +\abx@aux@read@bbl@mdfivesum{76D65A242EC496C9B4361AF646FF12CB} +\gdef \@abspage@last{3} diff --git a/recherches/ALDLoverAB/main.bbl b/recherches/ALDLoverAB/main.bbl new file mode 100644 index 0000000..1b062e4 --- /dev/null +++ b/recherches/ALDLoverAB/main.bbl @@ -0,0 +1,20 @@ +% $ biblatex auxiliary file $ +% $ biblatex bbl format version 3.3 $ +% Do not modify the above lines! +% +% This is an auxiliary file used by the 'biblatex' package. +% This file may safely be deleted. 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