3NF and BCNF Compared

Third normal form and boyce-codd normal form a comparison

Difference between 3NF and BCNF

Assume the following things;

A and B are set of attributes.

A is non-key attribute and B is the primary key.

FD – { A → B. }

The above Functional Dependency is about the dependency of primary key on a non-key attribute. This functional dependency is permitted in Third Normal Form (3NF). 3NF tries to identify and eliminate Non-key → Non-key dependency.

This Functional Dependency is not permitted in Boyce-Codd Normal Form (BCNF), because BCNF expects the determiner should be a candidate key. In our example, A is not a candidate key. This is why BCNF is termed as strict 3NF.

3NF is always achievable. BCNF is not. BCNF may result in Loss-less Join Decomposition and lead to loss of Dependency Preserving Decompositions.

Properties	3NF	BCNF
Achievability	Always achievable	Not always achievable
Quality of the tables	Less	More
Non-key Determinants	Can have non-key attributes as determinants	Cannot have.
Proposed by	Edgar F. Codd	Raymond F.Boyce and Edgar F.Codd jointly proposed
Decomposition	Loss-less join decomposition can be achieved	Sometimes Loss-less join decomposition cannot be achieved

Table 1 – 3NF – BCNF Comparisons

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Compare third normal form 3nf and boyce codd normal form bcnf