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# What is type 3 grammar? Explain its properties

Type 3 grammars are regular grammars that describe regular / formal languages.

These grammars contain production rules consisting of the following −

Only one non-terminal at the left hand side,

The right hand side has a single terminal and may or may not be followed by non terminals.

## Example

A → ε , A → a, A → b, A → aA etc.

## Types

There are two types of regular grammars namely −

Right linear / Right regular grammar

Left linear / Left regular grammar

Let us learn about these two types of grammar in detail.

## Right linear grammar

This is a regular grammar with the production rules of the form

A → α (or) A → α B

Where, A, B → non terminal symbols α → terminal symbol

These grammars are right-branching in nature, since the substitution is done for the right most non terminal, if available.

## Left linear grammar

This is a regular grammar with the production rules of the form −

A → α (or) A → B α

Where, A and B are non terminals and α is a terminal symbol.

Since the substitution is done for the leftmost non-terminal, these grammars are left branching in nature.

## Properties of Regular grammars

The regular grammars generates regular languages which are closed under the following −

Union

Concatenation

Intersection

Complementation

Difference

Reversal

Reversal

Closure

Homomorphism

Inverse homomorphism.