# Boyce-Codd Normal Form

**DOI:**https://doi.org/10.1007/978-1-4899-7993-3_1245-2

## 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 [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...

### Recommended Reading

- 1.Codd EF. Recent investigations in relational data base systems. In: Proceedings of IFIP congress; 1974, p. 1017–21.Google Scholar
- 2.Beeri C, Bernstein P. Computational problems related to the design of normal form relational schemas. ACM Trans Database Sys. 1979;4(1):30–59.CrossRefGoogle Scholar