Match the LIST-I with LIST-II
| LIST-I (Grammar) |
LIST-II (All productions are of the form) |
| A. Regular Grammar |
I. \(A \to aX\), where \(a \in T\) and \(X \in V^*\) |
| B. Unrestricted Grammar |
II. \(A \to xB, A \to x\) or \(A \to Bx, A \to x\) where \(A, B \in V\) and \(x \in T^*\) |
| C. Chomsky Normal Form |
III. \(x \to y\), where \(x \in (V \cup T)^+\) and \(y \in (V \cup T)^*\) |
| D. Greibach Normal Form |
IV. \(A \to BC\) or \(A \to a\), where \(A, B, C\) are in \(V\) and \(a\) is in \(T\). |
Choose the correct answer from the options given below:
1.A-II, B-III, C-I, D-IV
2.A-I, B-III, C-II, D-IV
3.A-II, B-III, C-IV, D-I ✓ Correct
4.A-II, B-IV, C-I, D-III
Solution
The correct answer is A-II, B-III, C-IV, D-I.
Key Points
- A. Regular Grammar → II
- Regular grammar productions are of the form: A → xB, A → x, A → Bx or A → ε where x ∈ T*.
- This matches statement II.
- B. Unrestricted Grammar → III
- Unrestricted grammar allows productions: x → y where x ∈ (V ∪ T)+ and y ∈ (V ∪ T)*.
- This matches statement III.
- C. Chomsky Normal Form → IV
- CNF productions are: A → BC or A → a.
- This matches statement IV.
- D. Greibach Normal Form → I
- GNF productions are: A → aX where a ∈ T and X ∈ V*.
- This matches statement I.
Additional Information
- Summary of Normal Forms:
- Regular Grammar → Type 3 grammar.
- Unrestricted Grammar → Type 0 grammar.
- Chomsky Normal Form → Binary or terminal productions.
- Greibach Normal Form → Starts with terminal.