ALDoverABv1
This commit is contained in:
Amaury JOLY
parent
87ef596364
commit
aefa847e9b
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recherches/ALDLoverAB/ABAL.pdf
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recherches/ALDLoverAB/ABAL.pdf
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recherches/ALDLoverAB/algo/index.tex
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recherches/ALDLoverAB/algo/index.tex
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We define $k$ as the id of the round \\
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the $getMax(..)$ function able to return the highest round played in the system.
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\begin{algorithm}[H]
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\DontPrintSemicolon
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\SetAlgoLined
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\KwIn{le message $m$}
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\BlankLine
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\While{true}{
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proves = READ() \\
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k = getMax(dump) + 1 \\
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APPEND(k || m) \\
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\If{PROVE(k)}{
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APPEND(k) \\
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return
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}
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}
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\caption{AB\_Broadcast}
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\end{algorithm}
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We define $k\_max$ as an intager \\
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$getMax(..)$ function able to return the highest round played in the system. \\
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% $proves_r$ as the sub set of proves with only the valid proves associated to the round r \\
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$proves_r \subseteq proves$ s.a. $\forall PROVE(x) \in proves_r$, x is in the form $r || m$ with $m$ who cannot be empty \\
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$proves_r^i$ is the $PROVE(r || m )$ operation submited by the process i if exist \\
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\begin{algorithm}[H]
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\DontPrintSemicolon
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\SetAlgoLined
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\BlankLine
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\While{true}{
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proves = READ() \\
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k\_max = getMax(proves) \\
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\For{r=k+1 \emph{\KwTo} k\_max}{
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APPEND(r)\\
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$proves_r$ = \{$\forall i, PROVE(r)_i \in READ()$\} \\
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\For{i = 1 \emph{\KwTo} $|P|$}{
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\If{$\exists PROVE(r)_i \in proves_r$}{
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AB\_Recv($m$ s.t. $PROVE(r || m) \in proves$)
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}
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}
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}
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}
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\caption{AB\_Listen}
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\end{algorithm}
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recherches/ALDLoverAB/intro/index.tex
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\subsubsection{Model Properties}
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The model is defined as Message-passing Aysnchronous. \\
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There is n process. Each process is associated to a unique unforgeable id $i$.\\
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Each process know the identity of all the process in the system\\
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Each process have a reliable communication channel with all the others process such as:
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\begin{itemize}
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\item send(m) is the send primitive
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\item recv(m) is the reception primitive
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\end{itemize}
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A message send is eventualy received\\
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The system is Crash-Prone. There is at most f process who can crash such as f < n.\\
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\subsubsection{AtomicBroadcast Properties}
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\begin{theorem}{AB\_broadcast Validity}
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if a message is sent by a correct process, the message is eventually received by all the correct process.
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\end{theorem}
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\begin{theorem}{AB\_receive Validity}
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if a message is received by a correct process, the message is eventually received by all the correct process.
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\end{theorem}
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\begin{theorem}{AB\_receive safety No creation}
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if a message is received by a correct process, the message was emitted by a correct porcess.
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\end{theorem}
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\begin{theorem}{AB\_receive safety No duplication}
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each message is received at most 1 time by each process.
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\end{theorem}
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\begin{theorem}{AB\_receive safety Ordering}
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$\forall m_1, m_2$ two messages, $\forall p_i, p_j$ two process. \\
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if AB\_recv(m1) and AB\_recv(m2) for $p_i, p_j$ \\
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and AB\_recv(m1) is before AB\_recv(m2) for $p_i$ \\
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so AB\_recv(m1) is before AB\_recv(m2) for $p_j$ \\
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\end{theorem}
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\subsubsection{DenyList Properties}
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\begin{theorem}{APPEND Validity}
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a APPEND(x) is valid iff the process p who sent the operation is such as $p \in \Pi_M$.
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And iff $x \in S$ where S is a set of valid values.
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\end{theorem}
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\begin{theorem}{PROVE Validity}
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a PROVE(x) is valid iff the process $p$ who sent the operation is such as $p \in \Pi_V$.
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And iff $\exists$ APPEND(x) who appears before PROVE(x) in Seq.
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\end{theorem}
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\begin{theorem}{PROGRESS}
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if an APPEND(x) is invoked, so there is a point in the linearization of the operations such as all PROVE(x) are valids.
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\end{theorem}
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\begin{theorem}{READ Validity}
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READ() return a list of tuples who is a random permutation of all valids PROVE() associated to the identity of the emiter process.
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\end{theorem}
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recherches/ALDLoverAB/main.aux
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recherches/ALDLoverAB/main.aux
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\relax
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\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
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\@nameuse{bbl@beforestart}
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\catcode `:\active
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\catcode `;\active
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\catcode `!\active
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\catcode `?\active
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\abx@aux@refcontext{nty/global//global/global/global}
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\providecommand \oddpage@label [2]{}
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\babel@aux{french}{}
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\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Model}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.1}Model Properties}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1.1.2}AtomicBroadcast Properties}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Algorithms}{1}{}\protected@file@percent }
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\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces AB\_Broadcast}}{2}{}\protected@file@percent }
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\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces AB\_Listen}}{2}{}\protected@file@percent }
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\abx@aux@read@bbl@mdfivesum{76D65A242EC496C9B4361AF646FF12CB}
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\gdef \@abspage@last{3}
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recherches/ALDLoverAB/main.bbl
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% $ biblatex auxiliary file $
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% $ biblatex bbl format version 3.3 $
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% This file may safely be deleted. It will be recreated by
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\endinput
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recherches/ALDLoverAB/main.bbl-SAVE-ERROR
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% $ biblatex auxiliary file $
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% $ biblatex bbl format version 3.3 $
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\author{JOLY Amaury \\ \textbf{Encadrants :} GODARD Emmanuel, TRAVERS Corentin}
|
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Loading…
Reference in New Issue
Block a user