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GATE | GATE-CS-2014-(Set-2) | Question 46
  • Last Updated : 03 Nov, 2017

Let <M> be the encoding of a Turing machine as a string over ∑= {0, 1}.  Let L = { <M> |M is a Turing machine that accepts a string of length 2014 }. Then, L is
(A) decidable and recursively enumerable
(B) undecidable but recursively enumerable
(C) undecidable and not recursively enumerable
(D) decidable but not recursively enumerable

Answer: (B)

Explanation: There are finite number of strings of length ‘2014’. So, a turing machine will take the input string of length ‘2014’ and test it.

If, input string is present in the language then turing machine will halt in final state .

But, if turing machine is unable to accept the input string then it will halt in non-final state or go in an infinite loop and never halt.
Thus, ‘L’ is undecidable and recursively enumerable .

Please comment below if you find anything wrong in the above post.

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