# Theory of Computation | Applications of various Automata

Automata is a machine that can accept the Strings of a *Language L* over an *input alphabet *.

So far we are familiar with the Types of Automata . Now, let us discuss the expressive power of Automata and further understand its Applications.

__Expressive Power of various Automata__:

The Expressive Power of any machine can be determined from the class or set of Languages accepted by that particular type of Machine. Here is the increasing sequence of expressive power of machines :

As we can observe that FA is less powerful than any other machine. It is important to note that DFA and NFA are of same power because every NFA can be converted into DFA and every DFA can be converted into NFA .

The Turing Machine i.e. TM is more powerful than any other machine.

(i) Finite Automata (FA) equivalence:

Finite Automata ≡ PDA with finite Stack ≡ TM with finite tape ≡ TM with unidirectional tape ≡ TM with read only tape

(ii) Pushdown Automata (PDA) equivalence:

PDA ≡ Finite Automata with Stack

(iii) Turing Machine (TM) equivalence:

Turing Machine ≡ PDA with additional Stack ≡ FA with 2 Stacks

The **Applications** of these Automata are given as follows:

**1. Finite Automata (FA) –**

- For the designing of lexical analysis of a compiler.
- For recognizing the pattern using regular expressions.
- For the designing of the combination and sequential circuits using Mealy and Moore Machines.
- Used in text editors.
- For the implementation of spell checkers.

- For designing the parsing phase of a compiler (Syntax Analysis).
- For implementation of stack applications.
- For evaluating the arithmetic expressions.
- For solving the Tower of Hanoi Problem.

**3. Linear Bounded Automata (LBA) –**

- For implementation of genetic programming.
- For constructing syntactic parse trees for semantic analysis of the compiler.

**4. Turing Machine (TM) –**

- For solving any recursively enumerable problem.
- For understanding complexity theory.
- For implementation of neural networks.
- For implementation of Robotics Applications.
- For implementation of artificial intelligence.

## Recommended Posts:

- Theory of Computation | Pushdown Automata
- Theory of Computation | Finite Automata Introduction
- Theory of Computation | Generating regular expression from finite automata
- Theory of Computation | Conversion from NFA to DFA
- TOC | Introduction of Theory of Computation
- Theory of Computation | Minimization of DFA
- Theory of Computation | L-graphs and what they represent
- Theory of Computation | Arden's Theorem
- Theory of computation | Halting Problem
- Theory of Computation | Chomsky Hierarchy
- Last Minute Notes - Theory of Computation
- Theory of Computation | Decidability and Undecidability
- Theory of Computation | Pumping Lemma
- Theory of Computation | Decidability table
- Theory of Computation | Relationship between grammar and language

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