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two fixes open in #93 #97

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Dec 17, 2024
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two fixes open in #93 #97

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8 changes: 8 additions & 0 deletions reports/ref.bib
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Expand Up @@ -44,6 +44,14 @@ @misc{tla-examples
note = {Accessed: 2024-10-25}
}

@misc{tla-paxos,
title = { {TLA}$^+$ specification of {Paxos} },
author = { Leslie Lamport },
howpublished = {\url{https://github.com/tlaplus/Examples/blob/master/specifications/Paxos/Paxos.tla}},
year = 2024,
note = {Accessed: 2024-12-17}
}

@article{DBLP:journals/lmcs/BansalBRT18,
author = {Kshitij Bansal and
Clark W. Barrett and
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7 changes: 2 additions & 5 deletions reports/spec4b.tex
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Expand Up @@ -37,18 +37,15 @@ \subsection{Constraints over set cardinalities}
\cdot T + 1$ set elements to show that Equation~(\ref{eq:card-comparison2})
holds true. This gives us a linear number of constraints, instead of a
quadratic one. For example, when $T=1$ and the set may contain up to~$n$
elements, the model checker produces $3 \cdot O(n)$ constraints to check
elements, the model checker produces $O(n)$ constraints to check
Equation~(\ref{eq:card-comparison2}). A similar optimization is used in the
specification of Tendermint~\cite{TendermintSpec2020}.

\subsection{Quorum sets}

To further optimize the constraints over set cardinalities, we have applied the
well-known pattern of replacing cardinality tests with quorum sets. For
example, this approach is used in the specification of Paxos\footnote{%
\tlap{} specification of Paxos:
\url{https://github.com/tlaplus/Examples/blob/master/specifications/Paxos/Paxos.tla}.}

example, this approach is used in the specification of Paxos~\cite{tla-paxos}.
To this end, we introduce quorum sets such as in Figure~\ref{fig:quorum-sets}.

\begin{figure}[!h]
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