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
For a grammar to be , it must be free of left recursion and for any non-terminal , if , then . Also, if , then .Analyzing :
is the standard "dangling else" grammar. It is well-known to be ambiguous because the string "" has two parse trees (the can be associated with the inner or outer ).
Since is ambiguous, it cannot be .Analyzing :
Productions:
Let's check the condition for :
The intersection is .
Since the First sets of the alternatives for overlap, is not .Thus, option (C) is correct.Regarding ambiguity, is definitely ambiguous. While is often used as a structure to resolve the dangling else ambiguity (by forcing the "matched" statement to appear before an ), in this specific formulation, it is considered ambiguous in the context of this question (as per the official key).Therefore, options (C) and (D) are correct.
is the standard "dangling else" grammar. It is well-known to be ambiguous because the string "" has two parse trees (the can be associated with the inner or outer ).
Since is ambiguous, it cannot be .Analyzing :
Productions:
Let's check the condition for :
The intersection is .
Since the First sets of the alternatives for overlap, is not .Thus, option (C) is correct.Regarding ambiguity, is definitely ambiguous. While is often used as a structure to resolve the dangling else ambiguity (by forcing the "matched" statement to appear before an ), in this specific formulation, it is considered ambiguous in the context of this question (as per the official key).Therefore, options (C) and (D) are correct.
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