1
GATE CSE 2015 Set 2
+1
-0.3
Consider the following statements.

$$\,\,\,$$ $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The complement of every Turing decidable language is Turing decidable
$$\,$$ $${\rm II}.\,\,\,\,\,\,\,\,\,$$ There exists some language which is in $$NP$$ but is not Turing decidable
$${\rm III}.\,\,\,\,\,\,\,\,\,$$ If $$L$$ is a language in $$NP,$$ $$L$$ is Turing decidable

Which of the above statements is/are true?

A
Only $${\rm I}$$$${\rm I}$$
B
Only $${\rm III}$$
C
Only $${\rm I}$$ and $${\rm II}$$
D
Only $${\rm I}$$ and $${\rm III}$$
2
GATE CSE 2015 Set 1
+1
-0.3

For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?

I. $${\overline L _1}$$ (complement of L1) is recursive
II. $${\overline L _2}$$ (complement of L2) is recursive
III. $${\overline L _1}$$ is context-free
IV. $${\overline L _1} \cup {L_2}$$ is recursively enumerable
A
I only
B
III only
C
III and IV only
D
I and IV only
3
GATE CSE 2014 Set 2
+1
-0.3
Let $$A\,\,{ \le _m}\,\,B$$ denotes that language $$A$$ is mapping reducible (also known as many-to-one reducible) to language $$B.$$ Which one of the following is FALSE?
A
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is recursive then $$A$$ is recursive.
B
If $$A\,\,{ \le _m}\,\,B$$ and $$A$$ is undecidable then $$B$$ is un-decidable.
C
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is recursively enumerable then $$A$$ is recursively enumerable.
D
If $$A\,\,{ \le _m}\,\,B$$ and $$B$$ is not recursively enumerable then $$A$$ is not recursively enumerable.
4
GATE CSE 2013
+1
-0.3
Which of the following statements is/are FALSE?
$$1.$$ For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine
$$2.$$ Turing recognizable languages are closed under union and complementation
$$3.$$ Turing decidable languages are closed under intersection and complementation
$$4.$$ Turing recognizable languages are closed under union and intersection
A
$$1$$ and $$4$$ only
B
$$1$$ and $$3$$ only
C
$$2$$ only
D
$$3$$ only
GATE CSE Subjects
EXAM MAP
Medical
NEET