Canonical Covers

• Checking every functional dependency hen data is updated is slow/expensive
• Therefore, canonical covers exist: F_c
  • Canonical covers have the same end result, but are shorter and cleaner
  • Notably, there can be multiple canonical covers for the same F
• Canonical covers remove bloat:
  • For instance:
    • If AB->C, but A alone is enough to tell you C, then B is extra
    • If A->BC, but C can already be figured out using other rules in the list, C is extra
• Ex:
  Given:

A->BC
B->C
A->B
AB->C

We can clean it up by doing the following:

# Combine
If A->BC and A->B, they can be combined into A->BC

# Check left sides
If A->B and B->C, we can prove C with A, so we can delete AB->C

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Currently, we have:
A->BC
B->C
A->B
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# Check right sides
As we have A->BC, A->B, and B->C, we can get to C through B already, so we can delete A->BC


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FINAL:
A->B
B->C
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