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remove RB for crash algorithms + some syntaxes fix in BFT algo

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Amaury JOLY
2026-03-16 09:15:07 +00:00
parent bee54232af
commit d629de3670
6 changed files with 179 additions and 192 deletions
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12
Recherche/BFT-ARBover/5_BFT_ARB/index.tex
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@@ -29,7 +29,7 @@ There are 3 operations : $\BFTPROVE(x), \BFTAPPEND(x), \BFTREAD()$ such that :
\paragraph{PROVE Anti-Flickering.} If the invocation of a operation $op = \BFTPROVE(x)$ by a correct process $p \in \Pi_V$ is invalid, then any $\BFTPROVE(x)$ operation that appears after $op$ in $\Seq$ is invalid.
\paragraph{READ Liveness.} Let $op = \BFTREAD()$ invoke by a correct process such that $R$ is the result of $op$. For all $(i, \PROVEtrace(x)) \in R$ there exist a valid invocation of $\BFTPROVE(x)$ by $p_i$.
\paragraph{READ Liveness.} Let $op = \BFTREAD()$ invoke by a correct process such that $R$ is the result of $op$. For all $(i, x) \in R$ there exist a valid invocation of $\BFTPROVE(x)$ by $p_i$.
\paragraph{READ Anti-Flickering.} Let $op_1, op_2$ two $\BFTREAD()$ operations that returns respectively $R_1, R_2$. Iff $op_1 \prec op_2$ then $R_2 \subseteq R_1$. Otherwise $R_1 \subseteq R_2$.
@@ -124,7 +124,7 @@ For each $U \in \mathcal{U}$, we instantiate one DenyList object $DL_U$ whose au
\end{lemma}
\begin{proof}
Let $R$ the result of a $READ()$ operation submit by any correct process. $(i, \PROVEtrace(x)) \in R$ implie that $\exists U^\star \in \mathcal{U}$ such that $(i, x) \in R^{U^\star}$ with $R^{U^\star}$ the result of $DL_{U^\star}.\READ()$. By \textbf{READ Validity} $(i, x) \in R^{U^\star}$ implie that there exist a valid $DL_{U^\star}.\PROVE_i(x)$. The for loop in the $\BFTPROVE(x)$ implementation return true iff there at least one valid $DL_{U}.\PROVE_i(x)$ for any $U \in \mathcal{U}$.
Let $R$ the result of a $READ()$ operation submit by any correct process. $(i, x) \in R$ implie that $\exists U^\star \in \mathcal{U}$ such that $(i, x) \in R^{U^\star}$ with $R^{U^\star}$ the result of $DL_{U^\star}.\READ()$. By \textbf{READ Validity} $(i, x) \in R^{U^\star}$ implie that there exist a valid $DL_{U^\star}.\PROVE_i(x)$. The for loop in the $\BFTPROVE(x)$ implementation return true iff there at least one valid $DL_{U}.\PROVE_i(x)$ for any $U \in \mathcal{U}$.
Hence because there exist a $U^\star$ such that $DL_{U^\star}.\PROVE_i(x)$, there exist a valid $\BFTPROVE_i(x)$.
@@ -189,18 +189,18 @@ For each $U \in \mathcal{U}$, we instantiate one DenyList object $DL_U$ whose au
\For{$r = 1, 2, \ldots$}{\nllabel{alg:main-loop}
\textbf{wait until} $\unordered \setminus \ordered \neq \emptyset$\;
$S \gets \unordered \setminus \ordered$;
$\RBcast(i, \texttt{PROP}, S, r)$\;
$\RBcast(\texttt{PROP}, S, \langle i, r \rangle)$\;
\textbf{wait until} $|\validated(r)| \geq n - t$\;\nllabel{alg:check-validated}
\BlankLine
\lForEach{$j \in \Pi$}{
$\BFTAPPEND(\langle j, r\rangle)$\;\nllabel{alg:append}
$\BFTAPPEND(\langle j, r\rangle)$\nllabel{alg:append}
}
\lForEach{$j \in \Pi$}{
$\send(j, \texttt{DONE}, r)$\;
$\send(\texttt{DONE}, r)$ \textbf{ to } $p_j$
}
\BlankLine
@@ -211,7 +211,7 @@ For each $U \in \mathcal{U}$, we instantiate one DenyList object $DL_U$ whose au
\BlankLine
$M \gets \bigcup_{j \in \winners[r]} \prop[r][j]$\;\nllabel{code:Mcompute}
$\ordered \gets \ordered \cdot \ordered(M)$\;
$\ordered \gets \ordered \cdot \order(M)$\;
}
\vspace{0.3em}