GATE CS 2024 Set 2 Q.65: Parsing and Syntax Analysis (LL and LR)

Consider the following augmented grammar, which is to be parsed with a SLR parser. The set of terminals is $\{a,b,c,d,\#,@\}$

S' \rightarrow S

S \rightarrow SS \mid Aa \mid bAc \mid Bc \mid bBa

A \rightarrow d\#

B \rightarrow @

Let $I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\})$ . The number of items in the set $\text{GOTO}(I_0, S)$ is ___________

Your answer

Official answer and solution

Official answer: 9
From: Official GATE 2024 answer key

Solution

Find the kernel items of $\text{GOTO}(I_0, S)$ by advancing the dot past $S$ in $I_0$ , then compute $\text{CLOSURE}$ by expanding nonterminals immediately following the dot.

In $I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\})$ $I_{0} = CLOSURE ({S^{'} \to ∙ S})$ , the items having the dot ( $\bullet$ $∙$ ) immediately before $S$ $S$ are:
- $S' \rightarrow \bullet S$
- $S \rightarrow \bullet SS$
Advancing the dot past $S$ $S$ gives the kernel items of $\text{GOTO}(I_0, S)$ $GOTO (I_{0}, S)$ (2 items):
1. $S' \rightarrow S\bullet$
2. $S \rightarrow S\bullet S$
Since the dot in $S \rightarrow S\bullet S$ immediately precedes nonterminal $S$ , $\text{CLOSURE}$ adds all $5$ productions of $S$ with a leading dot (5 items):
3. $S \rightarrow \bullet SS$
4. $S \rightarrow \bullet Aa$
5. $S \rightarrow \bullet bAc$
6. $S \rightarrow \bullet Bc$
7. $S \rightarrow \bullet bBa$
Because $S \rightarrow \bullet Aa$ has the dot before $A$ and $S \rightarrow \bullet Bc$ has the dot before $B$ , $\text{CLOSURE}$ also adds the productions of $A$ and $B$ (2 items):
8. $A \rightarrow \bullet d\#$
9. $B \rightarrow \bullet @$

Total number of LR(0) items in $\text{GOTO}(I_0, S)$ is $2 + 5 + 2 = 9$ .

Final answer

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

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 2 (CS2)
Question: 65 of 65
Section: Computer Science and Information Technology

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