Consider the productions $\text{A} \rightarrow \text{PQ}$ and $\text{A} \rightarrow \text{XY}$. Each of the five non-terminals A, P, Q, X, and Y has two attributes: $s$ is a synthesized attribute, and $i$ is an inherited attribute. Consider the following rules. Rule 1: P.$i$ = A.$i$ + 2, Q.$i$ = P.$i$ + A.$i$, and A.$s$ = P.$s$ + Q.$s$ Rule 2: X.$i$ = A.$i$ + Y.$s$ and Y.$i$ = X.$s$ + A.$i$ Which one of the following is TRUE?

In a Syntax-Directed Definition (SDD), an attribute grammar is L-attributed if each inherited attribute of a grammar symbol $X_j$ on the right-hand side of a production $A \to X_1 X_2 \dots X_n$ depends only on:

1. The inherited attributes of the parent non-terminal $A$.

2. The attributes (synthesized or inherited) of symbols $X_1, X_2, \dots, X_{j-1}$ appearing to the left of $X_j$.

3. Inherited attributes of $X_j$ itself, such that no cycles are formed.

Let us evaluate each rule:

• Rule 1 for $A \to PQ$:

  • $\text{P}.i = \text{A}.i + 2$: Inherited attribute of $\text{P}$ depends only on the parent's inherited attribute $\text{A}.i$. (Valid)

  • $\text{Q}.i = \text{P}.i + \text{A}.i$: Inherited attribute of $\text{Q}$ depends on $\text{P}.i$ (a symbol to the left of $\text{Q}$) and $\text{A}.i$ (parent). (Valid)

  • $\text{A}.s = \text{P}.s + \text{Q}.s$: Synthesized attribute of parent depends on attributes of its children. (Valid)

  Therefore, Rule 1 is L-attributed.

• Rule 2 for $A \to XY$:

  • $\text{X}.i = \text{A}.i + \text{Y}.s$: Inherited attribute of $\text{X}$ depends on $\text{Y}.s$, where $\text{Y}$ appears to the right of $\text{X}$. This violates the L-attributed definition.

  Therefore, Rule 2 is not L-attributed.

Hence, only Rule 1 is L-attributed, making (B) the correct option.