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Theory of Automata

Theory of Automata


The study of abstract machines which involves arithmetic operations, as well as the computational problems, that may be solved by using them. Automata is a branch of discrete mathematics (a part of mathematics and computer science as well). An automaton is a Greek word which actually means “self-acting”.

The automaton includes a variety of different states, and transitions. When automaton sees an input symbol, it starts a transition to another state, which is according to the rule of transition function (it takes the current state and the recent symbol as its input).

This theory of automata is also related to formal language theory. An automaton is a finite depiction of a formal language which can be an infinite set. Automata is often categorised by the class of formal language which they are able to recognize.

Automata play a vital role in the following:
  • Computation theory
  • Formal verification
  • Parsing
  • Artificial intelligence
  • Designing of compiler

An automaton is designed to process on some given sequence of input data in discrete time steps. At any point of time, the symbols that are given to the automaton as input forms a finite sequence of symbols, which comes to be known as a Word. An automaton consists of a finite group of states. At any time during the processing, the automaton is in some state or the other. At the time when input word is read, at that time the automaton is said to have come to a state of rest, and this state of rest is known to us as the final state. The acceptance or rejection of an input word depends on the final state. The group of all words accepted by an automaton is known as the language recognized by the automaton.

In a simpler way, an automaton is a mathematical object that receives a word as input and then makes a decision of accepting or rejecting it. An important role is played by the theory of automat in computational theory.


Input word:


A finite string of symbols are like q0, q1, q2... qn, where, qi ? ? is read by an automaton and is known as input word. The whole set of words is described by ?.

Continuous, Discrete, and hybrid automat:
The theory of automata usually defines the states of abstract machines but there also exist analog automata / hybrid continuous- discrete automata / continuous automata, all of these uses continuous time, analog data, or both of them.




Every automata theory model has an important role in a variety of applied areas. Finite automata are utilized in compiling, processing, and design of hardware. Artificial intelligence and programming languages makes use of context-free grammar (CFGs), initially CFGs were used for studying human languages. John Conway’s Game of Life is the best known example of the use of cellular automata in the area of biology.

Some types of automata:
  • Deterministic/nondeterministic finite state machine
  • Pushdown automaton
  • Turing machine
  • Linear bounded automaton
  • Rabin automaton
  • Streett automaton
  • Muller automaton
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