GATE 2026 CS1 Q.53: solution and answer

Official answer: A, B, DSource: Official answer key, GATE 2026 CS1 (IIT Guwahati)

1. Language of G1: from $D\to TV$ and $V\to V_1\text{id}\mid \text{id}$, $V$ derives ${\text{id}}^{+}$ (one or more ids), so $P=(\text{int}\mid \text{float}){\text{id}}^{+}$.

2. Language of G2: from $D\to D_1\text{id}\mid T\text{id}$, $D$ derives $T\text{id}{\text{id}}^{\ast }$, so $Q=(\text{int}\mid \text{float}){\text{id}}^{+}$. Hence $P=Q$ and (A) is true.

3. SDD2: every rule defines the head's attribute from attributes of body symbols ($D.\text{type}$ from $D_1.\text{type}$ or $T.\text{type}$; $T.\text{type}$ from a constant). The $\text{put}$ calls only read $D_1.\text{type}$ or $T.\text{type}$, and $\text{id.entry}$ is a lexical value supplied by the scanner. So every attribute is synthesized, SDD2 is S-attributed, and (B) is true.

4. SDD1: $V.\text{type}=T.\text{type}$ and $V_1.\text{type}=V.\text{type}$ define an attribute of a body symbol from the parent's or a left sibling's attribute, so $V.\text{type}$ is inherited and the definition is L-attributed. But $T.\text{type}$ and $D.\text{type}$ are defined from the head's own production body or a constant, so they are synthesized. SDD1 therefore does not contain only inherited attributes, and (C) is false.

5. Symbol table entries: in SDD1 each id receives $V.\text{type}$, which is copied from $T.\text{type}$ down the chain of $V$ nodes. In SDD2 each id receives $T.\text{type}$ (first id) or $D_1.\text{type}$ (later ids), which is the same declared type passed up the $D$ chain. In both, every id of a declaration is entered with the declared type, so the same entries are added and (D) is true.

6. Answer: A, B and D.