Functional Dependency

Functional Dependency is a fundamental concept in the field of Database Management Systems (DBMS). It is primarily used in relational databases to maintain data consistency and to help with the normalization process. In simple terms, a functional dependency describes a relationship between two sets of attributes in a database table.

Definition

A Functional Dependency (FD) occurs when the value of one attribute (or a group of attributes) determines the value of another attribute. It is denoted as:

A → B

This means that if two rows of a table have the same value for attribute A, they must also have the same value for attribute B.

Here,

A is called the determinant,
B is called the dependent attribute.

Real-Life Example

Imagine a table Students with the following columns:

StudentID	Name	Course
101	Riya	B.Tech
102	Aman	B.Sc
103	Riya	B.Tech

Here, StudentID → Name is a functional dependency because a student ID uniquely determines a student’s name.

However, Name → StudentID is not a functional dependency. As you can see, “Riya” appears more than once with different student IDs, so the name alone does not determine the student ID.

Types of Functional Dependencies

There are several types of functional dependencies in DBMS:

1. Trivial Functional Dependency

A functional dependency is trivial if the dependent is a subset of the determinant.

Example:

{StudentID, Name} → StudentID

This is trivial because StudentID is part of the left-hand side.

2. Non-Trivial Functional Dependency

It is non-trivial if the dependent is not a subset of the determinant.

Example:

StudentID → Name

Here, Name is not a part of StudentID.

3. Full Functional Dependency

An attribute is fully functionally dependent on a set of attributes if it is dependent on the entire set and not on any subset.

Example:

(StudentID, CourseCode) → Grade

If Grade depends on both StudentID and CourseCode, but not on each individually, then it’s a full dependency.

4. Partial Functional Dependency

It occurs when a dependent attribute is dependent on part of a composite key.

Example:

(StudentID, CourseCode) → StudentName

If StudentName depends only on StudentID, not on CourseCode, it’s a partial dependency. This needs to be removed in 2NF normalization.

5. Transitive Dependency

A transitive dependency occurs when:

A → B and B → C, then A → C

It indicates an indirect dependency, which is removed in 3NF (Third Normal Form).

Why is Functional Dependency Important?

Functional dependencies are crucial for:

Normalization

They help identify and eliminate redundancy in database tables. For example, knowing that StudentID → Name means we don’t need to repeat Name unnecessarily.

Data Integrity

By maintaining correct dependencies, we ensure that data updates, deletions, and insertions do not introduce inconsistencies.

Database Design

It helps to determine candidate keys, primary keys, and helps define normal forms for optimization.

Armstrong’s Axioms (Rules of Functional Dependencies)

Armstrong’s Axioms are a set of inference rules used to derive all the functional dependencies from a given set. The three main rules are:

Reflexivity:
If Y is a subset of X, then X → Y
Augmentation:
If X → Y, then XZ → YZ
Transitivity:
If X → Y and Y → Z, then X → Z

Additional rules derived from these:

Union: If X → Y and X → Z, then X → YZ
Decomposition: If X → YZ, then X → Y and X → Z
Pseudo Transitivity: If X → Y and YZ → W, then XZ → W

These rules are important for reasoning about dependencies and for normal form analysis.