GATE CS 2014 Set 3 — Question 45
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Theory of Computation → Context-Free Languages → Ambiguity
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Question
Which one of the following problems is undecidable?
Correct answer
(A) Deciding if a given context-free grammar is ambiguous.
Solution
The problem of determining whether a given Context-Free Grammar (CFG) is ambiguous is known to be undecidable. There is no algorithm that can determine for an arbitrary CFG whether it is ambiguous or not.Let's analyze the other options:
- (B) Membership problem for CFGs (is string in
L(G)?) is decidable (e.g., using the CYK algorithm). - (C) Emptiness problem for CFGs (is ?) is decidable (check if the start symbol can generate any terminal string).
- (D) Finiteness problem for CFGs (is
L(G)finite?) is decidable (check for loops in the dependency graph of variables that can generate terminals).
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