# Boyce-Codd Normal Form

**DOI:**https://doi.org/10.1007/978-0-387-39940-9_1245

## Synonyms

## Definition

Let *R*(*A*_{1},*...*,*A*_{n}) be a relation schema and Σ a set of functional dependencies over *R*(*A*_{1},...,*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 [2], Codd pointed out that this normal form was developed by Raymond F. Boyce and himself.) in [2]. 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...

## Recommended Reading

- 1.Beeri C. and Bernstein P. Computational Problems Related to the Design of Normal Form Relational Schemas. ACM Trans. Database Sys., 4(1):30–59, 1979.CrossRefGoogle Scholar
- 2.Codd E.F. Recent Investigations in Relational Data Base Systems. In Proc. IFIP Congress. 1974, pp. 1017–1021.Google Scholar