Normal Forms & BCNF
Subject: Database Management Systems
Boyce-Codd Normal Form and relational schema decomposition.
Concept Summary
Database normalization organizes attributes to reduce data redundancy and update anomalies. BCNF addresses functional dependencies where a non-prime or prime attribute is functionally determined by a non-superkey. By enforcing that every determinant X in X -> Y must be a superkey, BCNF eliminates all redundancy based on FDs.
Key Revision Rules & Formulas
- A relation R is in BCNF if for every non-trivial functional dependency X -> Y, X is a super key.
- BCNF is strictly stronger than 3NF.
- 3NF permits X -> Y where Y is a prime attribute even if X is not a super key; BCNF eliminates this exception.
- BCNF decomposition guarantees zero redundancy from functional dependencies.
Common Exam Pitfalls
- Assuming BCNF always preserves functional dependencies: BCNF decomposition is always lossless-join, but may NOT always preserve all functional dependencies (whereas 3NF decomposition always preserves FDs).
- Confusing Candidate Key with Super Key: A super key is any set of attributes containing a candidate key.
Sample Practice Questions
Question 1: A relation R is in Boyce-Codd Normal Form (BCNF) if for every non-trivial functional dependency X -> Y, which condition must hold?
- Y is a prime attribute
- X is a super key
- X is a candidate key subset
- Y is a super key
Explanation: BCNF is stricter than 3NF and requires that for every functional dependency X -> Y, X must be a super key.