1
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider the language :
$${L_1}\, = \left\{ {w\,{w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$
$${L_2}\, = \left\{ {w\, \ne {w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$ where $$ \ne $$ is a special symbol
$${L_3}\, = \left\{ {w\,w\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$

Which one of the following is TRUE?

A
$${L_1}$$ $$=$$ is a deterministic $$CFL$$
B
$${L_2}$$ $$=$$ is a deterministic $$CFL$$
C
$${L_3}$$ is a $$CFL,$$ but not a deterministic $$CFL$$
D
$${L_3}$$ IS A DETERMINISTIC $$CFL$$
2
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
3
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Consider three decision problems $${P_1},$$ $${P_2}$$ and $${P_3}.$$ It is known that $${P_1}$$ is decidable and $${P_2}$$ is un-decidable. Which of the following is TRUE?
A
$${P_3}$$ is decidable if $${P_1}$$ is reducible to $${P_3}$$
B
$${P_3}$$ is in-decidable if $${P_3}$$ is reducible to $${P_2}$$
C
$${P_3}$$ is un-decidable if $${P_2}$$ is reducible to $${P_3}$$
D
$${P_3}$$ is decidable if $${P_3}$$ is reducible to $${P_2}'s$$ complement
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