3NF

Third normal form (3NF) is a database normalization standard aimed at reducing update anomalies by ensuring that non-prime attributes depend on candidate keys directly rather than through other non-prime attributes. A prime attribute is one that belongs to some candidate key of the relation; a candidate key is a minimal set of attributes that functionally determines all attributes of the relation.

A relation is in 3NF if, for every nontrivial functional dependency X → Y that holds in the relation, either X is a superkey, or Y is a prime attribute. Equivalently, every non-prime attribute must be non-transitively dependent on every candidate key. This condition allows certain dependencies to exist where the dependent attribute is prime, which BCNF would not permit.

3NF sits between 2NF and BCNF. It is stricter than 2NF in addressing transitive dependencies, but less strict than BCNF, which requires every nontrivial dependency to have a superkey on the left side. In practice, 3NF is commonly used because it reduces redundancy while often preserving dependencies during decomposition.

Decomposition into 3NF typically involves splitting a relation when a non-key attribute depends on a non-superkey in a way that violates the 3NF condition. A standard synthesis approach creates relations from the problematic functional dependencies, ensuring a lossless join and, in many cases, dependency preservation.

Example: R(A, B, C) with A → B and B → C has A as a candidate key, but B → C violates 3NF. Decomposing into R1(A, B) and R2(B, C) yields relations in 3NF.