GATE CS 2024 Set 1 — Question 38
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Compiler Design → Syntax Analysis → First & Follow Sets
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Question
Consider the following grammar , with as the start symbol. The grammar has three incomplete productions denoted by (1), (2), and (3).The set of terminals is . The FIRST and FOLLOW sets of the different non-terminals are as follows..Which one of the following options CORRECTLY fills in the incomplete productions?
Correct answer
(A) (1) S arrow Rf (2) T arrow ε (3) R arrow cTR
Solution
We are given the FIRST sets for the non-terminals:
Let's analyze the incomplete productions based on these sets.1. Analyze Production (1) for :
The production contributes to .
The missing part (1) must contribute the remaining elements of , which are .
The existing productions contribute and to .
The missing part (2) must contribute to match .
The existing production contributes .
The missing part (3) must contribute to match .
Let's analyze the incomplete productions based on these sets.1. Analyze Production (1) for :
The production contributes to .
The missing part (1) must contribute the remaining elements of , which are .
- Option (B) & (C): . This starts with the terminal . Thus, it adds to , but it cannot add . So, (B) and (C) are incorrect.
- Option (A) & (D): . Since , this production adds (from ) and, because is nullable (), it also adds . Thus, contributes both and . This matches the requirement.
The existing productions contribute and to .
The missing part (2) must contribute to match .
- Option (A): . This correctly adds to .
- Option (D): . This would add to . However, is not in the given . Thus, (D) is incorrect.
The existing production contributes .
The missing part (3) must contribute to match .
- Option (A): . This starts with , satisfying the condition.
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