Introduction of Finite Automata (original) (raw)

Last Updated : 7 Mar, 2026

Finite automata are abstract machines used to recognize patterns in input sequences, forming the basis for understanding regular languages in computer science.

• Consist of states, transitions, and input symbols, processing each symbol step-by-step.
• If ends in an accepting state after processing the input, then the input is accepted; otherwise, rejected.
• Finite automata come in deterministic (DFA) and non-deterministic (NFA), both of which can recognize the same set of regular languages.
• Widely used in text processing, compilers, and network protocols.

Figure: Features of Finite Automata

Features of Finite Automata

• **Input: Set of symbols or characters provided to the machine.
• **Output: Accept or reject based on the input pattern.
• **States of Automata: The conditions or configurations of the machine.
• **State Relation: The transitions between states.
• **Output Relation: Based on the final state, the output decision is made.

Formal Definition of Finite Automata

A finite automaton can be defined as a tuple:

{ Q, Σ, q, F, δ }, where:

• Q: Finite set of states
• Σ: Set of input symbols
• q: Initial state
• F: Set of final states
• δ: Transition function

Types of Finite Automata

There are two types of finite automata:

1. Deterministic Finite Automata (DFA)
2. Non-Deterministic Finite Automata (NFA)

1. Deterministic Finite Automata (DFA)

A DFA is represented as {Q, Σ, q, F, δ}. In DFA, for each input symbol, the machine transitions to one and only one state. DFA does not allow any null transitions, meaning every state must have a transition defined for every input symbol.

DFA consists of 5 tuples {Q, Σ, q, F, δ}.
Q : set of all states.
Σ : set of input symbols. ( Symbols which machine takes as input )
q : Initial state. ( Starting state of a machine )
F : set of final state.
δ : Transition Function, defined as δ : Q X Σ --> Q.

**Example: Construct a DFA that accepts all strings ending with 'a'.

Given:

Σ = {a, b},

Q = {q0, q1},

F = {q1}

Fig 1. State Transition Diagram for DFA with Σ = {a, b}

In this example, if the string ends in 'a', the machine reaches state q1, which is an accepting state.

2. Non-Deterministic Finite Automata (NFA)

NFA is similar to DFA but includes the following features:

• It can transition to multiple states for the same input.
• It allows null (ϵ) moves, where the machine can change states without consuming any input.

**Example: Construct an NFA that accepts strings ending in 'a'.

Given:

Σ = {a, b},

Q = {q0, q1},

F = {q1}

Fig 2. State Transition Diagram for NFA with Σ = {a, b}

State Transition Table for above Automaton,

In an NFA, if any transition leads to an accepting state, the string is accepted.

NFA vs DFA