GATE CS 2025 Set 2 — Question 51
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Compiler Design → Context-Free Languages → Ambiguity
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Question
Consider two grammars and with the production rules given below:where are the terminals.Which of the following option(s) is/are CORRECT?
Correct answer
(C) G₁ and G₂ are not LL(1).; (D) G₁ and G₂ are ambiguous.
Solution
LL(1) check. A grammar is LL(1) only if, for every non-terminal, the FIRST sets of its alternatives are disjoint (and no other FIRST/FOLLOW conflict exists).: both and begin with , so FIRST sets overlap and is not LL(1). is also the classic dangling-else grammar and is ambiguous: has two parse trees (the can attach to either ).: FIRST and FIRST. They share , so is not LL(1). is also ambiguous. Take .
- Tree 1: , and the inner with and (itself ).
- Tree 2: with the final and the inner (i.e. with , ).
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