1
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-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
A
decidable and recursively enumerable
B
un-decidable but recursively enumerable
C
un-decidable and not recursively enumerable
D
decidable but not recursively enumerable
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
If $$L$$ and $$\overline L $$ are recursively enumerable then $$L$$ is
A
Regular
B
Context-free
C
Context-sensitive
D
Recursive.
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-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?
A
$${L_1} \cap {L_2}$$ is deterministic $$CFL$$
B
$${L_3} \cap {L_1}$$ is recursive
C
$${L_1} \cup {L_2}$$ is context-free
D
$${L_1} \cap {L_2} \cap {L_3}$$ is recursively enumerable
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$
Let $$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,d\left( s \right)\,} \right.} \right.$$ mod $$5=2$$ and $$d(s)$$ mod $$\left. {7 \ne 4} \right\}$$

Which of the following statement is true?

A
$$L$$ is recursively enumerable, but not recursive
B
$$L$$ is recursive, but not context-free
C
$$L$$ is context-free, but not regular
D
$$L$$ is regular
GATE CSE Subjects
Software Engineering
Web Technologies
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