Given the following syntax directed translation rules:

Rule 1: R→ABR→AB [B.i=R.i−1;A.i=B.iR.i=A.i+1;B.i=R.i−1;A.i=B.iR.i=A.i+1;]
Rule 2: P→CDP→CD [P.i=C.i+D.i;D.i=C.i+2P.i=C.i+D.i;D.i=C.i+2]
Rule 3: Q→EFQ→EF [Q.i=E.i+F.i;Q.i=E.i+F.i;]

Which ONE is the CORRECT option among the following?

The correct option is: Rule 1 is neither S-attributed nor L-attributed; Rule 2 is not S-attributed and is L-attributed; Rule 3 is S-attributed and L-attributed.

To determine the correct classification of each Syntax-Directed Translation (SDT) rule, let us first review the definitions of S-attributed and L-attributed definitions:

1. S-attributed definition:
An SDD is S-attributed if it uses only synthesized attributes. In a syntax-directed definition, a synthesized attribute at a node is computed from the attributes of its children. In grammar terms, for a production $X\to Y_1{Y}_2...Y_n$, only the attribute of the left-hand side symbol $X$ is computed, and it depends solely on the attributes of the right-hand side symbols $Y_1,Y_2...Y_n$.

2. L-attributed definition:
An SDD is L-attributed if every attribute is either synthesized, or inherited with the restriction that the inherited attributes of a sibling symbol $Y_j$ on the right-hand side of a production $X\to Y_1{Y}_2...Y_n$ can depend only on:
- The inherited attributes of the left-hand side parent head $X$.
- The attributes (either synthesized or inherited) of sibling symbols $Y_1,Y_2...Y_{j-1}$ that lie to the left of $Y_j$.
Note that every S-attributed definition is also an L-attributed definition, because S-attributed definitions do not have any inherited attributes and thus trivially satisfy the constraints of L-attributed definitions.

Let us analyze each rule step-by-step:

Analysis of Rule 1:
Production: $R\to AB$
Semantic Rules:
$B.i=R.i-1$
$A.i=B.i$
$R.i=A.i+1$

Looking at the action $A.i=B.i$, the attribute of the symbol $A$ (which is to the left of $B$) depends on the attribute of the symbol $B$ (which is to the right of $A$). This right-to-left dependency violates the constraint of L-attributed definitions. Furthermore, since it contains inherited attributes (such as $B.i$ and $A.i$), it is not S-attributed. Thus, Rule 1 is neither S-attributed nor L-attributed.

Analysis of Rule 2:
Production: $P\to CD$
Semantic Rules:
$P.i=C.i+D.i$
$D.i=C.i+2$

Here, the inherited attribute of $D$ (which is $D.i$) depends on $C.i$ (an attribute of its left sibling symbol $C$). This is a valid dependency for an L-attributed definition. The attribute $P.i$ of the head is synthesized from the right-hand side attributes. Because it contains the inherited attribute $D.i$ on the right-hand side, it is not S-attributed. Therefore, Rule 2 is not S-attributed but is L-attributed.

Analysis of Rule 3:
Production: $Q\to EF$
Semantic Rules:
$Q.i=E.i+F.i$

In this rule, the attribute of the left-hand side head $Q$ is computed using only the attributes of the right-hand side symbols $E$ and $F$. There are no inherited attributes computed for any of the right-hand side symbols. This makes the rule S-attributed. Since all S-attributed definitions are a subset of L-attributed definitions, Rule 3 is both S-attributed and L-attributed.