Boyce-Codd Normal Form

Synonyms

BCNF

Definition

Let R(A₁, …,A_n) be a relation schema and Σ a set of functional dependencies over R(A₁,…,A_n). Then (R, Σ) is said to be in Boyce-Codd normal form (BCNF) if for every nontrivial functional dependency X → A implied by Σ, it holds that X is a superkey for R.

Key Points

In order to avoid update anomalies in database schemas containing functional dependencies, BCNF was introduced by Codd in [1] (Codd pointed out in [1] that this normal form was developed by Raymond F. Boyce and himself.). This normal form is defined in terms of the notion of superkey as shown above. For example, given a relation schema R(A, B, C) and a set of functional dependencies Σ = {AB → C, C → B}, it does not hold that (R(A, B, C), Σ) is in BCNF since C is not a superkey for R. On the other hand, (S (A, B, C), Γ) is in BCNF if Γ = {A → BC}, since A is a superkey for S in this case.

It should be noticed that relation schema R(A, B, C) above is in 3NF if Σ = {AB → C, C → B}, although this schema...