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# What are different types of finite automata?

Finite automata is an abstract computing device. It is a mathematical model of a system with discrete inputs, outputs, states and a set of transitions from state to state that occurs on input symbols from the alphabet Σ.

## Formal definition of Finite Automata

Finite automata is defined as a 5-tuples

**M=(Q, Σ, δ,q0,F)**

Where,

- Q: Finite set called states.
- Σ: Finite set called alphabets.
- δ: Q × Σ → Q is the transition function.
- q0 ∈ Q is the start or initial state.
- F: Final or accept state.

### Types

The different types of Finite Automata are as follows −

- Finite Automata without output
- Deterministic Finite Automata (DFA).
- Non-Deterministic Finite Automata (NFA or NDFA).
- Non-Deterministic Finite Automata with epsilon moves (e-NFA or e-NDFA).

- Finite Automata with Output
- Moore machine.
- Mealy machine.

## Definition of different automata (DFA)

A Deterministic Finite automata is defined as a 5-tuples

**M=(Q, Σ, δ,q0,F)**

Where,

- Q: Finite set called states.
- Σ: Finite set called alphabets.
- δ: Q × Σ → Q is the transition function.
- q0 ∈ Q is the start or initial state.
- F: Final or accept state.

## Non-deterministic finite automata (NFA)

NFA also have five states which are same as DFA, but with different transition function, as shown follows −

**δ: Q X Σ -> 2Q**

Non-deterministic finite automata is defined as a 5 tuple,

**M=(Q, Σ, δ,q0,F)**

Where,

- Q: Finite set of states
- Σ: Finite set of the input symbol
- q0: Initial state
- F: Final state
- δ: Transition function: Q X Σ -> 2Q

## Mealy Machine

The Mealy machine described by 6 tuples (Q, q0, Σ, O, δ, λ')

Where,

- Q: Finite set of states
- q0: Initial state of machine
- Σ: Finite set of input alphabet
- O: Output alphabet
- δ: Transition function where Q × Σ → Q
- λ': Output function where Q × Σ →O

## Moore Machine

Moore machine described by 6 tuples (Q, q0, Σ, O, δ, λ)

where,

- Q: Finite set of states
- q0: Initial state of machine
- Σ: Finite set of input symbols
- O: Output alphabet
- δ: Transition function where Q × Σ → Q
- λ: Output function where Q → O

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