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GATE | GATE-CS-2017 (Set 1) | Question 62

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  • Difficulty Level : Basic
  • Last Updated : 11 Oct, 2021
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Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A* to B* .We say f is computable if there exists a Turning machine M which given an input x in
A*, always halts with f(x) on its tape. Let Lf denotes the language {x#f(x)|x∈A*}. Which of the following statements is true?
(A) f if computable if and only if Lf is recursive.
(B) f if computable if and only if Lf is recursive enumerable.
(C) if f is computable then Lf is recursive, but not conversely.
(D) if f is computable then Lf is recursively enumerable, but not conversely.


Answer: (A)

Explanation: This definition is given as Halting of Turing Machine. Every recursive language is computable, but converse may not be true.



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