What are different types of finite automata?

Data Structure AlgorithmsComputer ScienceComputers

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
raja
Published on 11-Jun-2021 17:10:26
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