Question

Define Boyce-Codd normal form. How does it differ from 3NF? Why is it consid. ered a stronger form of \(3 \mathrm{NF}\) ?

Short answer

Boyce-Codd Normal Form (BCNF) is a database normalization rule that reduces redundancy and dependency by ensuring that functional dependency is on a superkey. It differs from Third Normal Form (3NF) because BCNF is stricter, requiring that for all dependencies X -> Y, X is a superkey. This makes BCNF stronger than 3NF because it removes more redundancy and prevents certain types of anomalies.

Step-by-step solution

Defining BCNF

Boyce-Codd Normal Form (BCNF) is a design rule in database normalization that is used to reduce redundancy and dependency of data. It is a more advanced normalization form compared to the Third Normal Form (3NF). BCNF was developed by Raymond F. Boyce and Edgar F. Codd to address certain types of anomalies not dealt with by 3NF. BCNF states that for any functional dependency \(A \rightarrow B\), A must be a super key.

Comparing BCNF and 3NF

In 3NF, a table is in 3NF if it is in 2NF and no non prime attribute transitively depends on any key. However, the Boyce-Codd Normal Form (BCNF) is stricter than 3NF. Story is, when a table is in BCNF than it is also in 3NF. While in BCNF, a table is in BCNF if it’s in 3NF and for every one of its dependencies X -> Y, X is a super key.

Why BCNF is Stronger than 3NF

BCNF is considered stronger than 3NF because BCNF is strict and removes all functional dependencies except trivial dependencies. BCNF eliminates more redundancy than 3NF. In other words, a relational database schema is in BCNF if, and only if, for every one of its dependencies X -> Y, X is a superkey.

Key concepts

Database Normalization

Database normalization is a fundamental concept in database design, aiming to organize a database in a way that reduces redundancy and dependency. This systematic approach involves dividing a database into two or more tables and defining relationships between the tables.

The ultimate goal is to isolate data so that additions, deletions, and modifications of a field can be made in just one table and then propagated through the rest of the database using the defined relationships.

• First Normal Form (1NF): Eliminates duplicate columns from the same table.
• Second Normal Form (2NF): Addresses the concept of removing subsets of data that apply to multiple rows of a table and placing them in separate tables.
• Third Normal Form (3NF): Ensures that every non-prime attribute is non-transitively dependent on every key of the table.

Normalization often continues to further forms such as BCNF, each addressing more specific types of redundancy.

Functional Dependency

Functional Dependency is a relationship that exists when one attribute uniquely determines another. In database design, this is crucial as it ensures the integrity of the data. It lays the foundation for all normalization stages.

A functional dependency is denoted as \(A \rightarrow B\), which implies that if we know the value of attribute A, we can uniquely determine the value of attribute B. The attribute A is called the determinant, and B is the dependent.

Types of Functional Dependencies:

• Full Functional Dependency: A functional dependency is full if removal of any attribute in A means the dependency no longer exists.
• Transitive Dependency: When a non-prime attribute depends on another non-prime attribute rather than depending directly on the primary key.
• Trivial Dependency: A dependency of an attribute on a full set of attributes, including itself, which is always true.

Functional dependencies are key to understanding and defining the form of normalization that a database is in.

Third Normal Form (3NF)

The Third Normal Form (3NF) is a level of database normalization designed to reduce the duplication of data and ensure referential integrity by organizing fields in a database into tables. To satisfy 3NF, a database table must first meet all the criteria of the Second Normal Form (2NF).

Additionally, 3NF requires that all the attributes in a table, which are not composite keys, be dependent on the primary key, ensuring no transitive dependency. In simpler terms, all non-key attributes should not depend on any other non-key attributes.

Example:

If a table with customer data has fields like Customer ID, Customer Name, and Customer Zip Code, and Customer Zip Code uniquely determines Customer State, this would violate 3NF because Customer State depends on Customer Zip Code, not on the primary key Customer ID. This issue is resolved by moving Customer State to a related table with a relation to Customer Zip Code, removing the indirect dependency.