1
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0

Which of the following statements is/are TRUE?

A
Every subset of a recursively enumerable language is recursive.
B
If a language L and its complement $$\overline L $$ are both recursively enumerable, then L must be recursive.
C
Complement of a context-free language must be recursive.
D
If L1 and L2 are regular, then L1 $$\cap$$ L2 must be deterministic context-free.
2
GATE CSE 2020
MCQ (Single Correct Answer)
+1
-0.33
Consider the language
L = { $${a^n}|n \ge 0$$ } $$ \cup $$ { $${a^n}{b^n}|n \ge 0$$ }
and the following statements.

I. L is deterministic context-free.
II. L is context-free but not deterministic context-free.
III. L is not LL(k) for any k.

Which of the above statements is/are TRUE?
A
I only
B
II only
C
I and III only
D
III only
3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Consider the following types of languages: $${L_1}:$$ Regular, $${L_2}:$$ Context-free, $${L_3}:$$ Recursive, $${L_4}:$$ Recursively enumerable. Which of the following is/are TRUE?

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\overline {{L_3}} \cup {L_4}$$ is recursively enumerable
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ $$\overline {{L_2}} \cup {L_3}$$ is recursive
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ $$L_1^ * \cap {L_2}$$ is context-free
$$\,\,\,{\rm I}V.\,\,\,\,\,\,\,$$ $${L_1} \cup \overline {{L_2}} $$ is context-free

A
$${\rm I}$$ only
B
$${\rm I}$$ and $${\rm III}$$ only
C
$${\rm I}$$ and $${\rm IV}$$ only
D
$${\rm I},$$ $${\rm II}$$ and $${\rm III}$$ only
4
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+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
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