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Theory Of Computation | Types of Automata and Representation

The validation of a string for its membership in a language are handled by automata.

An automaton acts as a acceptor of a string for a given language

This is an example for an automaton which accepts all strings containing at least one 'a'.

These circles are known as states. So X and Y are states.

Circle with dual boundary (here Y) is final state and one with unmarked arrow is initial state(here X).

Consider the string "baba",

Initially we are at X, on seeing first alphabet 'b' the automaton loop back to X itself( Edge with alphabet 'b' point to X itself).

On seeing next alphabet 'a', the state transition happens and reaches at new state Y.

Once we reaches at state Y, both 'a' and 'b' loop back to the same state.

So the string "baba" finally reaches as state Y

Since the Y is the final state of this automaton, we can conclude that the sting "baba" belongs to the language represented by the given automaton.

All finite automata are classified as follows :

  1. Automata with output
    • Moore Machine
    • Mealy Machine
  2. Automata without output
    • Deterministic Finite Automata (DFA)
    • Non-deterministic Finite Automata (NFA)
    • Epsilon NFA (ε-NFA)

We will discuss about each of of them in detail in upcoming posts.


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