Which of the following NFA is valid for the given DFA?
Match List I with List II
| List I (Grammar Type) | List II (Production Form) |
|---|---|
| A. Type 3 Grammar | IV. $V \rightarrow V\Sigma \mid \Sigma$ |
| B. Type 2 Grammar | I. $V \rightarrow (V \cup \Sigma)^{*}$ |
| C. Type 1 Grammar | II. $\lambda A \beta \rightarrow \lambda\,\gamma\,\beta,\;(\lambda,\beta)\in (V\cup\Sigma)^{*}$ |
| D. Type 0 Grammar | III. $(V\cup\Sigma)^{*} \rightarrow (V\cup\Sigma)^{*}$ |
Why: Type-3 (regular) → right-linear (IV); Type-2 (context-free) → $V \to (V\cup\Sigma)^*$ (I); Type-1 (context-sensitive) → context-preserving form (II); Type-0 (unrestricted) → any string to any string (III).
| Label | Productions | Note |
|---|---|---|
| A | S → Ab aS → aA A → a | LHS “aS” has a terminal → not CFG |
| B | S → Ab A → Sa A → a | All rules are left-linear (V→Vt or V→t) → regular |
| C | S → AS S → aA A → a | CFG, not regular (non-linear: V→VV) |
| D | S → Ab S → aA A → a | CFG; mixes left/right-linear → not regular |
| E | S → Sb A → Aa A → ε | From start S no terminal string → L(S)=∅ (regular) |
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