Consider the following two syntax-directed definitions SDD1 and SDD2 for type declarations. $D$ is the start symbol, and $int$, $float$ and $id$ are the three terminals. The non-terminal $V_1$ is the same as $V$ and the non-terminal $D_1$ is the same as $D$. Here, the subscript is used to differentiate the grammar symbols on the two sides of a production. The function $put$ updates the symbol table with the type information for an identifier. Let P and Q be the languages specified by grammars G1 and G2, respectively. Which of the following statements is/are true?

Let us analyze each statement based on the definitions:

1. Language Equivalence (Option A):

   • Grammar $G_1$:

     $$D \to T\,V$$

     $$T \to \text{int} \mid \text{float}$$

     $$V \to V_1\,\text{id} \mid \text{id}$$

     Here, $V$ generates one or more identifiers, $\text{id}^+$. Thus, $L(G_1) = (\text{int} \mid \text{float})\,\text{id}^+$.

   • Grammar $G_2$:

     $$D \to D_1\,\text{id} \mid T\,\text{id}$$

     $$T \to \text{int} \mid \text{float}$$

     Here, $D$ expands to $T\,\text{id}\,\text{id}^* = (\text{int} \mid \text{float})\,\text{id}^+$.

   • Since both grammars generate strings composed of a type specifier followed by one or more identifiers, the languages $P$ and $Q$ are identical. Hence, (A) is true.

2. Attribute Classification of SDD2 (Option B):

   • In SDD2, the attributes evaluated are $T.\text{type}$ (from terminals $\text{int}/\text{float}$) and $D.\text{type}$ (from child $D_1$ or child $T$).

   • Since every attribute is synthesized from the children in the parse tree, SDD2 contains only synthesized attributes and is an S-attributed SDD. Hence, (B) is true.

3. Attribute Classification of SDD1 (Option C):

   • In SDD1, $D.\text{type}$ and $T.\text{type}$ are synthesized attributes, while $V.\text{type}$ is an inherited attribute ($V.\text{type} = T.\text{type}$).

   • SDD1 contains both synthesized and inherited attributes, so it does not contain *only* inherited attributes. Hence, (C) is false.

4. Symbol Table Entries (Option D):

   • In SDD1, the type synthesized at $T$ is passed down via inherited attribute $V.\text{type}$ to all identifiers, and put(id.entry, V.type) is invoked for each identifier.

   • In SDD2, the type is propagated up synthesized via $D.\text{type}$, and put(id.entry, D_1.type) or put(id.entry, T.type) is invoked for each identifier.

   • In both cases, each identifier declared in the statement is entered into the symbol table with its corresponding data type. Hence, (D) is true.

Thus, statements A, B, and D are correct.