BCNF

BCNF, or Boyce-Codd Normal Form, is a normal form used in relational database design. A relation R is in BCNF if every non-trivial functional dependency X -> Y that holds on R has X as a superkey of R (trivial dependencies are exempt). Equivalently, for any non-trivial FD X -> Y, X must functionally determine all attributes of R.

BCNF is a stricter condition than Third Normal Form (3NF). Every BCNF relation is also in 3NF, but not every 3NF relation is in BCNF. The stricter requirement can require decomposing a relation to eliminate violations, which may in turn affect dependency preservation.

A simple illustration: a relation R(A, B, C) with the dependency A -> B. Here A+ = {A, B}, so A is not a superkey for R, and the FD A -> B violates BCNF. Decomposition along this dependency into R1(A, B) and R2(A, C) yields two relations that can be in BCNF: in R1, A is a key for the attributes A and B; in R2, A serves as a key for A and C.

A standard decomposition approach for a violating FD X -> Y is to replace R with R1 = X ∪ Y and R2 = R − Y. This decomposition is lossless if X -> Y holds in R. However, BCNF decompositions do not always preserve all functional dependencies, unlike some 3NF designs which aim to retain more dependencies.

BCNF remains a fundamental tool for reducing redundancy and update anomalies, with the trade-off that more aggressive fragmentation may complicate queries and, in some cases, lose certain dependencies.