Calculate Minimal Cover (Canonical Cover)

• Page 325 in book (PDF page 354)
• Example in DBS4 slides p 69

Left Reduction

• If A is on the left side, let $NL =LeftSide - A$ and check if $NL \to RightSide$
• $NL$: New Left
• Remember: only check pairs, as singletons would become empty and meaningless
  • This explanation is probably not correct, but makes sense
• To do so, compute the closure of NL under the set of functional dependencies and check if all attributes in the closure is also in the right side
  • To compute closure under a functional dependency:
  • Check which attributes can be inferred from the current attribute(s).
  • This is recursive, so if $A \to B$, then $A$ can continue inferring what $B$ infers.
  • Remember: An attribute can always infer itself
  • Remember: The set of functional dependencies temporarily has $A$ removed from the chosen functional dependency

Right Reduction

• If $A$ is on the right side, let $F^*$ be the set of functional dependencies without $A$ in its place
• Alternative explanation: Remove $A$ from it place in the current chosen functional dependency
• Check if the chosen dependency/the dependency $A$ was in still can infer to $A$
• Do this by computing the closure of the chosen dependency under F

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Last update: June 1, 2020