What is type 3 grammar? Explain its properties

Data Structure AlgorithmsComputer ScienceComputers

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.

raja
Published on 15-Jun-2021 11:49:48
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