GATE CSE 2014 Set 1 | Recursively Enumerable Language and Turing Machine Question 13 | Theory of Computation

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GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

-0.6

Let $$L$$ be a language and $$\overline L $$ be its complement. Which one of the following is NOT a viable possibility?

Neither $$L$$ nor $$\overline L $$ is recursively enumerable (r.e).

One of $$L$$ and $$\overline L $$ is r.e. but not recursive; the other is not r.e.

Both $$L$$ and $$\overline L $$ are r.e. but not recursive.

Both $$L$$ and $$\overline L $$ are recursive.

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

Let $$ < M > $$ be the encoding of a Turing machine as a string over $$\sum { = \left\{ {0,1} \right\}.} $$
Let $$L = \left\{ { < M > \left| M \right.} \right.$$ is a Turing machine that accepts a string of length $$\left. {2014} \right\}.$$ Then, $$L$$ is

decidable and recursively enumerable

un-decidable but recursively enumerable

un-decidable and not recursively enumerable

decidable but not recursively enumerable

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

If $$L$$ and $$\overline L $$ are recursively enumerable then $$L$$ is

Regular

Context-free

Context-sensitive

Recursive.

GATE CSE 2006

MCQ (Single Correct Answer)

-0.6

Let $${L_1}$$ be a regular language, $${L_2}$$ be a deterministic context-free language and $${L_3}$$ a recursively enumerable, but not recursive, language. Which one of the following statement is false?

$${L_1} \cap {L_2}$$ is deterministic $$CFL$$

$${L_3} \cap {L_1}$$ is recursive

$${L_1} \cup {L_2}$$ is context-free

$${L_1} \cap {L_2} \cap {L_3}$$ is recursively enumerable

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