UGC-NET | UGC NET CS 2018 Dec – II | Question 33

Consider the following problems:

• (i) Whether a finite automaton halts on all inputs?
• (ii) Whether a given Context Free Language is Regular?
• (iii) Whether a Turing Machine computes the product of two numbers?

Which one of the following is correct ?
(A) Only (ii) and (iii) are undecidable problems
(B) (i), (ii) and (iii) are undecidable problems
(C) Only (i) and (ii) are undecidable problems
(D) Only (i) and (iii) are undecidable problems

Answer: (A)
Explanation: A decision problem P is said to be decidable (i.e., have an algorithm) if the language L of all yes instances to P is decidable.

Membership problem of finite finite automaton is decidable.

Only (ii) and (iii) are undecidable problems.

Option (A) is correct.

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