[DMDB] Completed normal forms, start query optimization

semester4/dmdb/parts/02_theory-background/00_functional-dependencies/00_intro.tex

@@ -1,4 +1,5 @@
 \subsection{Functional Dependency}
+\label{sec:functional-dependency}
 As with relational algebra, we again define a schema to be a relation, e.g. $\cR(A:D_A, B:D_B, C:D_C, D: D_D)$,
 with an instance of it being $R \subseteq D_A \times D_B \times D_C \times D_D$.
 
@@ -12,9 +13,10 @@ and $R \vdash \alpha \rightarrow \beta$ if the same applies syntactically (i.e.
 \inlineintuition This means that there is a function that maps the values of columns $\alpha$ to the values of columns $\beta$.
 
 
-\inlinedefinition $\alpha \subseteq \R$ is a \bi{superkey} if and only if $\alpha \rightarrow \cR$.
+\inlinedefinition $\alpha \subseteq \R$ is a \gls{superkey} if and only if $\alpha \rightarrow \cR$.
 
-\inlineintuition This means that if we know the values of columns $\alpha$, we know the value of the rest of the columns in $\cR$
+\inlineintuition This means that if we know the values of columns $\alpha$, we know the value of the rest of the columns in $\cR$.
+It is a superset of some candidate keys (see \ref{sec:relations-keys})
 
 
 \inlinedefinition $\alpha \rightarrow \beta$ is minimal if and only if $\forall A \in \alpha : (\alpha - \{ A \}) \centernot{\rightarrow} \beta$.

semester4/dmdb/parts/02_theory-background/00_functional-dependencies/04_closure.tex

@@ -26,7 +26,7 @@ We can use that to check the following:
     \item $F \vdash \alpha \rightarrow \gamma$: Calculate $\alpha^+$ and check $\gamma \in \alpha^+$
     \item $F \vdash G$: For each $\alpha \rightarrow \gamma \in G$, check $F \vdash \alpha \rightarrow \gamma$
     \item $F$ equivalent to $G$: Check $F \vdash G$ and $G \vdash F$
-    \item $K \subseteq \cR$ superkey for $F$: Check $F \vdash K \rightarrow \cR$:
+    \item $K \subseteq \cR$ \gls{superkey} for $F$: Check $F \vdash K \rightarrow \cR$:
 \end{itemize}