GATE CS 2017 Set 1 Q.17 (CS Q.17): Parsing and Syntax Analysis (LL and LR)

Consider the following grammar:

P \to x Q R S

Q \to y z \mid z

R \to w \mid \epsilon

S \to y

What is $\text{FOLLOW}(Q)$ ?

$\{R\}$

$\{w\}$

$\{w, y\}$

$\{w, \$\}$

Official answer and solution

Official answer: C
From: Official GATE 2017 answer key

Solution

Compute $\text{FOLLOW}(Q)$ using the standard First and Follow set construction rules for context-free grammars.

Given grammar productions:

P \to x Q R S

Q \to y z \mid z

R \to w \mid \epsilon

S \to y

Non-terminal $Q$ appears on the right-hand side of $P \to x Q R S$ .
By the definition of FOLLOW sets, $\text{FOLLOW}(Q)$ contains everything in $\text{FIRST}(R S)$ except $\epsilon$ .

Compute $\text{FIRST}(R)$ and $\text{FIRST}(S)$ :

\text{FIRST}(R) = \{w, \epsilon\}

\text{FIRST}(S) = \{y\}

Since $\epsilon \in \text{FIRST}(R)$ :

\text{FIRST}(R S) = (\text{FIRST}(R) \setminus \{\epsilon\}) \cup \text{FIRST}(S) = \{w\} \cup \{y\} = \{w, y\}

Since $\text{FIRST}(S)$ does not contain $\epsilon$ , $\text{FIRST}(R S)$ does not derive $\epsilon$ . Therefore:

\text{FOLLOW}(Q) = \{w, y\}

This matches Option C.

Final answer

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

Source

Paper: GATE 2017 Computer Science and Information Technology (CS) Session 1
Question: 17 of 65, printed as CS Q.17
Section: Computer Science and Information Technology

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