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prerequisite is a set (#132)
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daiagi authored Nov 5, 2024
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4 changes: 2 additions & 2 deletions text/accumulation.tex
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Expand Up @@ -52,11 +52,11 @@ \subsection{History and Queuing}

The newly available work-reports, $\mathbf{W}$, are partitioned into two sequences based on the condition of having zero prerequisite work-reports. Those meeting the condition, $\mathbf{W}^!$, are accumulated immediately. Those not, $\mathbf{W}^Q$, are for queued execution. Formally:
\begin{align}
\mathbf{W}^! &\equiv [ w \mid w \orderedin \mathbf{W}, (w_x)_\mathbf{p} = \none \wedge w_\wr¬srlookup = \{\} ] \\
\mathbf{W}^! &\equiv [ w \mid w \orderedin \mathbf{W}, |(w_x)_\mathbf{p}| = 0 \wedge w_\wr¬srlookup = \{\} ] \\
\mathbf{W}^Q &\equiv E(\sq{
D(w) \mid
w \orderedin \mathbf{W},
(w_x)_\mathbf{p} \ne \none \vee w_\wr¬srlookup \ne \{\}
|(w_x)_\mathbf{p}| > 0 \vee w_\wr¬srlookup \ne \{\}
}, \accumulatedcup)\!\!\!\!\\
D(w) &\equiv (w, \{(w_x)_\mathbf{p}\} \cup \keys{w_\wr¬srlookup})
\end{align}
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