diff --git a/docs/constructions.tex b/docs/constructions.tex index 066cad023750f8317f80adffec965fd655fbc44f..30d4807c58f05b84caa67b7cdb41e21841ca2dfb 100644 --- a/docs/constructions.tex +++ b/docs/constructions.tex @@ -253,7 +253,8 @@ We obtain the following frame-preserving update: % \end{proof} -\subsection{Authoritative}\label{sec:auth} +\subsection{Authoritative} +\label{sec:auth-cmra} Given a CMRA $M$, we construct a monoid $\authm(M)$ modeling someone owning an \emph{authoritative} element $x$ of $M$, and others potentially owning fragments $\melt \le_M x$ of $x$. We assume that $M$ has a unit $\munit$, and hence its core is total. @@ -286,7 +287,7 @@ We then obtain \end{mathpar} \subsection{STS with tokens} -\label{sec:stsmon} +\label{sec:sts-cmra} Given a state-transition system~(STS, \ie a directed graph) $(\STSS, {\stsstep} \subseteq \STSS \times \STSS)$, a set of tokens $\STST$, and a labeling $\STSL: \STSS \ra \wp(\STST)$ of \emph{protocol-owned} tokens for each state, we construct an RA modeling an authoritative current state and permitting transitions given a \emph{bound} on the current state and a set of \emph{locally-owned} tokens.