Canonical Cover

 In the case of updating the database, the responsibility of the system 

is to check whether the existing functional dependencies are getting 

violated during the process of updating. In case of a violation of 

functional dependencies in the new database state, the rollback of 

the system must take place.

A canonical cover or irreducible a set of functional dependencies 

FD is a simplified set of FD that has a similar closure as the original 

set FD.

Extraneous attributes

An attribute of an FD is said to be extraneous if we can remove it 

without changing the closure of the set of FD.

Example: Given a relational Schema R( A, B, C, D) and set of 

Function Dependency FD = { B → A, AD → BC, C → ABD }. 

Find the canonical cover?

Solution: Given FD = { B → A, AD → BC, C → ABD }, now 

decompose the FD using decomposition rule( Armstrong Axiom ).

1. B → A

2. AD → B ( using decomposition inference rule on AD → 

BC)

3. AD → C ( using decomposition inference rule on AD → 

BC)

4. C → A ( using decomposition inference rule on C → 

ABD)

5. C → B ( using decomposition inference rule on C → 

ABD)

6. C → D ( using decomposition inference rule on C → 

ABD)

Now set of FD = { B → A, AD → B, AD → C, C → A, C → B, C 

→ D }

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