Given the following syntax directed translation rules: Rule 1: $R \to AB \{B.i = R.i - 1; A.i = B.i; R.i = A.i + 1;\}$ Rule 2: $P \to CD \{P.i = C.i + D.i; D.i = C.i + 2;\}$ Rule 3: $Q \to EF \{Q.i = E.i + F.i;\}$ Which ONE is the CORRECT option among the following?

To determine whether each syntax-directed definition (SDD) rule is S-attributed or L-attributed, we apply the standard definitions:

1. S-attributed SDD: Uses only synthesized attributes (i.e., attributes of the non-terminal on the LHS are computed solely from attributes of the children on the RHS).

2. L-attributed SDD: Allows both synthesized and inherited attributes. For any production $A \to X_1 X_2 \dots X_n$, an inherited attribute of $X_j$ may depend only on:

   • Inherited attributes of the head $A$, and/or

   • Attributes of symbols $X_1, X_2, \dots, X_{j-1}$ appearing to the left of $X_j$.

   *(Every S-attributed SDD is also an L-attributed SDD).*

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### Analysis of Each Rule:

• Rule 1: $R \to AB \{B.i = R.i - 1; A.i = B.i; R.i = A.i + 1;\}$

  • In $A.i = B.i$, the attribute of the symbol $A$ depends on $B$, which lies to its right. This violates the L-attributed property.

  • Since it contains inherited attributes ($B.i$ and $A.i$), it is also not S-attributed.

  • Therefore, Rule 1 is neither S-attributed nor L-attributed.

• Rule 2: $P \to CD \{P.i = C.i + D.i; D.i = C.i + 2;\}$

  • $P.i = C.i + D.i$ computes a synthesized attribute for the head $P$ from children $C$ and $D$.

  • $D.i = C.i + 2$ computes an inherited attribute for $D$ using $C$, which is strictly to the left of $D$. This satisfies the L-attributed condition.

  • Because it includes the inherited attribute $D.i$, it is not S-attributed.

  • Therefore, Rule 2 is not S-attributed and is L-attributed.

• Rule 3: $Q \to EF \{Q.i = E.i + F.i;\}$

  • $Q.i$ is computed solely from the attributes of its children $E$ and $F$.

  • This uses only synthesized attributes, so it is S-attributed.

  • Every S-attributed grammar is also L-attributed.

  • Therefore, Rule 3 is S-attributed and L-attributed.

Matching these classifications with the choices gives Option (C) as the correct answer.