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Which of the followings is a regular grammar?

Which of the followings is a regular grammar? Correct Answer S → abA, A → baB, B → aA, B → bb

The correct answer is option 1.

Concept:

A regular grammar is a grammar that is right-regular or left-regular. Regular grammar is also called Type-3 grammar.

By definition following are equal, Regular lanuage= Type-3 language =Regular expressions =Right linear grammar= Left linear grammar= DFA= NFA=ε-NFA.

Consider V= Non-terminal and T-terminal.

Type-3:

V→VT*, V→T* or V→T*V, V→T*

Type-2:

X→Y here X= only one non-terminal, Y=( V ∪ T)*(any combinations).

Type-1:

X→Y here X,Y=( V ∪ T)*(any combinations) and X<= Y.

Type-0:

X→Y here X,Y=( V ∪ T)*(any combinations).

Option 1:S → abA, A → baB, B → aA, B → bb

True, It is in regular grammar. It follows  V→T*V, V→T*.

Option 2: S → abB, A → aaBb, B → bbAa, A → λ 

False, It is not regular grammar but is Type-2 grammar or Context-free grammar. And follows X→Y here X= only one non-terminal, Y=( V ∪ T)*(any combinations).

Option 3: S → aSb, S → SS, S → λ 

False, It is not regular grammar but is Type-2 grammar or Context-free grammar. And follows X→Y here X= only one non-terminal, Y=( V ∪ T)*(any combinations).

Option 4: S → aSa, S → bSb, S → λ

False, It is not regular grammar but is Type-2 grammar or Context-free grammar. And follows X→Y here X= only one non-terminal, Y=( V ∪ T)*(any combinations).

Hence the correct answer is S → abA, A → baB, B → aA, B → bb.

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