GATE CS 2024 Set 2 Q.40: Parsing and Syntax Analysis (LL and LR)

Consider the following context-free grammar where the start symbol is $S$ and the set of terminals is $\{a,b,c,d\}$ .

S \rightarrow AaAb \mid BbBa

A \rightarrow cS \mid \epsilon

B \rightarrow dS \mid \epsilon

The following is a partially-filled LL(1) parsing table.

Which one of the following options represents the CORRECT combination for the numbered cells in the parsing table?

Note: In the options, "blank" denotes that the corresponding cell is empty.

(1) $S \rightarrow AaAb$ (2) $S \rightarrow BbBa$ (3) $A \rightarrow \epsilon$ (4) $B \rightarrow \epsilon$

(1) $S \rightarrow BbBa$ (2) $S \rightarrow AaAb$ (3) $A \rightarrow \epsilon$ (4) $B \rightarrow \epsilon$

(1) $S \rightarrow AaAb$ (2) $S \rightarrow BbBa$ (3) blank (4) blank

(1) $S \rightarrow BbBa$ (2) $S \rightarrow AaAb$ (3) blank (4) blank

Official answer and solution

Solution

Compute $\text{FIRST}(AaAb)$ , $\text{FIRST}(BbBa)$ , $\text{FOLLOW}(A)$ , and $\text{FOLLOW}(B)$ .

FIRST sets for productions of $S$ :
- Since $\text{FIRST}(A) = \{c, \epsilon\}$ , we have $\text{FIRST}(AaAb) = (\text{FIRST}(A) - \{\epsilon\}) \cup \{a\} = \{c, a\}$ . Therefore, cell (1) (row $S$ , column $c$ ) contains $S \rightarrow AaAb$ .
- Since $\text{FIRST}(B) = \{d, \epsilon\}$ , we have $\text{FIRST}(BbBa) = (\text{FIRST}(B) - \{\epsilon\}) \cup \{b\} = \{d, b\}$ . Therefore, cell (2) (row $S$ , column $d$ ) contains $S \rightarrow BbBa$ .
FOLLOW sets for $\epsilon$ -productions of $A$ and $B$ :
- In $S \rightarrow AaAb$ , the first $A$ is followed by terminal $a$ and the second $A$ is followed by terminal $b$ , so $\text{FOLLOW}(A) = \{a, b\}$ . Since $A \rightarrow \epsilon$ , cell (3) (row $A$ , column $b$ ) contains $A \rightarrow \epsilon$ .
- In $S \rightarrow BbBa$ , the first $B$ is followed by terminal $b$ and the second $B$ is followed by terminal $a$ , so $\text{FOLLOW}(B) = \{a, b\}$ . Since $B \rightarrow \epsilon$ , cell (4) (row $B$ , column $a$ ) contains $B \rightarrow \epsilon$ .

Final answer

Option (A)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.