1
GATE CSE 2022
MCQ (More than One Correct Answer)
+2
-0.67

Which of the following is/are undecidable?

A
Given two Turing machines M1 and M2, decide if L(M1) = L(M2).
B
Given a Turing machine M, decide if L(M) is regular.
C
Given a Turing machine M, decide if M accepts all strings.
D
Given a Turing machine M, decide if M takes more than 1073 steps on every string.
2
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67

For a Turing machine M, {M} denotes an encoding of M. Consider the following two languages.

L1 = {(M) | M takes more than 2021 steps on all inputs}

L2 = {(M) | M takes more than 2021 steps on some input}

Which one of the following options is correct?

A
Both L1 and L2 are undecidable.
B
L1 is undecidable and L2 is decidable.
C
L1 is decidable and L2 is undecidable.
D
Both L1 and L2 are decidable.
3
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
The set of all recursively enumerable languages is
A
closed under complementation.
B
closed under intersection.
C
a subset of the set of all recursive languages
D
an uncountable set.
4
GATE CSE 2018
MCQ (Single Correct Answer)
+2
-0.6
Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the language accepted by a machine $$M.$$

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ For an unrestricted grammar $$G$$ and a string $$W,$$ whether $$w \in L\left( G \right)$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ Given a Turing machine $$M,$$ whether $$L(M)$$ is regular
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ Given two grammars $${G_1}$$ and $${G_2}$$, whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ Given an $$NFA$$ $$N,$$ whether there is a deterministic $$PDA$$ $$P$$ such that $$N$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\\,\,\,$$and $$P$$ accept the same language.

Which one of the following statements is correct?

A
Only $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ are undecidable
B
Only $${\rm III}$$ is undecidable
C
Only $${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ are undecidable
D
Only $${\rm I}$$, $${\rm II}$$ and $${\rm III}$$ are undecidable
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