Database Normalization (BCNF)

Boyce-Codd Normal Form (BCNF) is a higher level of database normalization that addresses certain anomalies that might still exist in databases normalized up to 3NF. To achieve BCNF, a database should already be in 3NF. BCNF ensures that for every non-trivial functional dependency X -> Y, X must be a superkey. Let’s continue using the Student Course Registration Database example and work towards achieving BCNF:

Recap: Current Database State (3NF)

We have the following tables:

Students Table:

StudentID	StudentName
1	John
2	Jane
3	Alex

CourseDetails Table:

CourseID	CourseName	Instructor
101	Math	Prof. Smith
102	Physics	Prof. Johnson
103	Chemistry	Prof. Davis

StudentRegistrations Table:

StudentID	CourseID
1	101
1	102
2	101
3	103

Step 1: Identify Violations of BCNF

BCNF focuses on ensuring that non-trivial functional dependencies have superkeys as their left-hand sides. In our current structure, we have a functional dependency CourseID -> CourseName, Instructor in the CourseDetails table. However, CourseID is not a superkey; both CourseID and CourseName are needed to uniquely identify a course.

Step 2: Create a New Table

We need to create a new table with a candidate key that includes CourseID and CourseName, allowing us to remove the functional dependency violation.

CoursesNew Table:

CourseID	CourseName
101	Math
102	Physics
103	Chemistry

CourseInstructors Table:

CourseID	Instructor
101	Prof. Smith
102	Prof. Johnson
103	Prof. Davis

Step 3: Update Original Table

Remove the CourseName and Instructor columns from the CourseDetails table.

CourseDetails Table (BCNF):

CourseID
101
102
103

Step 4: Update Dependencies

Update the StudentRegistrations table to reference the new CoursesNew and CourseInstructors tables.

StudentRegistrations Table (BCNF):

StudentID	CourseID
1	101
1	102
2	101
3	103

Conclusion: The database is now in Boyce-Codd Normal Form (BCNF). We have resolved the violation of BCNF by splitting the CourseDetails table into CoursesNew and CourseInstructors tables. This ensures that every non-trivial functional dependency has a superkey as its left-hand side.

Keep in mind that achieving BCNF doesn’t necessarily mean your database is fully optimized for all use cases. Depending on your specific requirements and the complexity of your data, further normalization or denormalization might be necessary to strike the right balance between data integrity and performance.