Computer Sciences > Gate 2017 Set-1 > Recursive Language
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.

Correct : a

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computability theory recursive languages recursive enumerable languages GATE computer science 2017 Turing machine language Lf definition computable function recursive vs r.e. languages

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