GATE | GATE-CS-2007 | Question 6
Which of the following problems is undecidable? 
(A) Membership problem for CFGs
(B) Ambiguity problem for CFGs.
(C) Finiteness problem for FSAs.
(D) Equivalence problem for FSAs.
A set is closed under an operation means when we operate an element of that set with that operator we get an element from that set.
Here, CFG generates a CFL and set of all CFLs is the set. But ambiguity is not an operation and hence we can never say that CFG is closed under such operation.
Only ambiguity problem for CFGs are undecidable.
Thus, option (B) is correct.
Please comment below if you find anything wrong in the above post.
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