GATE CS 2025 Set 2 Q12 — Syntax-directed Translation

To determine the classification of each syntax-directed translation (SDT) rule, we use the definitions of $S$-attributed and $L$-attributed definitions:

• $S$-attributed SDD: Uses only synthesized attributes (attributes of the parent are computed from the attributes of its children).
• $L$-attributed SDD: Allows both synthesized and inherited attributes. However, an inherited attribute of a child on the right-hand side can only depend on the attributes of the parent or the siblings to its left.

Let's analyze each rule:

1. Rule 1 ($R \rightarrow A B$): The action A.i = B.i defines the attribute of child $A$ using the attribute of child $B$, which lies to its right. This violates the $L$-attributed condition. Since it uses inherited attributes, it is also not $S$-attributed. Thus, Rule 1 is neither $S$-attributed nor $L$-attributed.
2. Rule 2 ($P \rightarrow C D$): The action D.i = C.i + 2 defines the inherited attribute of $D$ using its left sibling $C$, which is allowed in $L$-attributed. The action P.i = C.i + D.i defines the head's attribute using its children, which is also allowed. Since it defines an inherited attribute of a child ($D.i$), it is not $S$-attributed. Thus, Rule 2 is not $S$-attributed and is $L$-attributed.
3. Rule 3 ($Q \rightarrow E F$): The action Q.i = E.i + F.i only defines the attribute of the head $Q$ using the attributes of its children. This behaves purely as a synthesized attribute. Thus, Rule 3 is both $S$-attributed and $L$-attributed.

Hence, the correct option is C.