1
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.
2
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
3
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
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let $${L_1}$$ be a recursive language, and Let $${L_2}$$ be a recursively enumerable but not a recursive language. Which one of the following is TRUE?
A
$$\overline {{L_1}} $$ is recursive and $$\overline {{L_2}} $$ is recursively enumerable
B
$$\overline {{L_1}} $$ is recursive and $$\overline {{L_2}} $$ is not recursively enumerable
C
$$\overline {{L_1}} $$ and $$\overline {{L_2}} $$ are recursively enumerable
D
$$\overline {{L_1}} $$ is recursively enumerable and $$\overline {{L_2}} $$ is recursive
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