Solution

Statement: The Correct answer is Option 3.

Explanation:

A. Type 3 Grammar:

• Type 3 Grammar is also known as Regular Grammar. It generates regular languages which are accepted by finite automata.
• The rules of this grammar are of the form V → (VUΣ)*, where V is a non-terminal, U is a terminal, and Σ represents the alphabet.
• Therefore, it matches with II.

B. Type 2 Grammar:

• Type 2 Grammar is also known as Context-Free Grammar. It generates context-free languages which are accepted by pushdown automata.
• The rules of this grammar are of the form λνβ → λ(VUE)*β, where (λ, β) ∈ (VU Σ)*.
• Therefore, it matches with I.

C. Type 1 Grammar:

• Type 1 Grammar is also known as Context-Sensitive Grammar. It generates context-sensitive languages which are accepted by linear-bounded automata.
• The rules of this grammar are of the form (VUE)* → (VUE)*.
• Therefore, it matches with III.

D. Type 0 Grammar:

• Type 0 Grammar is also known as Unrestricted Grammar. It generates recursively enumerable languages which are accepted by Turing machines.
• The rules of this grammar are of the form V → VΣΙΣ, where V represents non-terminals and ΣΙΣ represents terminals.
• Therefore, it matches with IV.

Final Matching:

• A → II
• B → I
• C → III
• D → IV

Correct Answer: Option 3