diff --git a/reports/ref.bib b/reports/ref.bib index 4c55b83..ea21f4e 100644 --- a/reports/ref.bib +++ b/reports/ref.bib @@ -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 diff --git a/reports/spec4b.tex b/reports/spec4b.tex index 30232ae..91f3341 100644 --- a/reports/spec4b.tex +++ b/reports/spec4b.tex @@ -37,7 +37,7 @@ \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}. @@ -45,10 +45,7 @@ \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]