Regular expression to Regular grammar

RGPV 2020   
How can we construct regular grammar from regular expression? 

Ans. Lets take an regular expresion example: 0*(1(0+1))*

Now convert above example in to regular language.

0*(1(0+1))*

Conver above regular expression into Right linear regular grammar in step by step.

Step 01:

S --> 0S

Step 02:

S --> 0S | A | ∈

 

Step 03:

S --> 0S | A | ∈

A --> 1B

Step 04:

S --> 0S | A | ∈

A --> 1B

B --> 0A | 1A | 0 | 1

Conver above regular expression into Left linear regular grammar in step by step.

Step 01:

S --> A | ∈

Step 02:

S --> A | ∈

A --> A10 | A11 | B

Step 03:

S --> A | ∈

A --> A10 | A11 | B

B --> B0 | 0