1
GATE CSE 2015 Set 3
+2
-0.6
Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible to $${L_2}$$ , which in turn is polynomial time reducible to language $${L_4}$$ . Which of the following is/are true?

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P$$ or $$\,\,\,{L_3} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P,$$ and only $$\,\,\,{L_3} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}V.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_1} \in P$$ and $$\,\,\,{L_3} \in P$$

A
$${\rm I}$$$${\rm I}$$ only
B
$${\rm III}$$ only
C
$${\rm I}$$ and $${\rm IV}$$ only
D
$${\rm I}$$ only
2
GATE CSE 2014 Set 3
+2
-0.6
Which one of the following problems is un-decidable?
A
Deciding if a given context-free grammar is ambiguous.
B
Deciding if a given string is generated by a given context-free grammar.
C
Deciding if the language generated by a given context-free grammar is empty.
D
Deciding if the language generated by a given context-free grammar is finite.
3
GATE CSE 2013
+2
-0.6
Which of the following is/are undecidable?
$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$
$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \sum {{}^ * } ?$$
$$3.$$ $$M$$ is a Turing Machine. Is $$L(M)$$ regular?
$$4.$$ $$A$$ is a $$DFA$$ and $$N$$ is an $$NFA.$$
Is $$L(A)=L(N)?$$
A
$$3$$ only
B
$$3$$ and $$4$$ only
C
$$1,2$$ and $$3$$ only
D
$$2$$ and $$3$$ only
4
GATE CSE 2005
+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
GATE CSE Subjects
EXAM MAP
Medical
NEET