1
GATE CSE 2022
MCQ (More than One Correct Answer)
+2
-0

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 2019
MCQ (Single Correct Answer)
+2
-0.67

Consider the following sets :

S1. Set of all recursively enumerable languages over the alphabet $\{0,1\}$

S2. Set of all syntactically valid C programs

S3. Set of all languages over the alphabet $\{0,1\}$

S4. Set of all non-regular languages over the alphabet $\{0,1\}$

Which of the above sets are uncountable?

A
S1 and S2
B
S3 and S4
C
S2 and S3
D
S1 and S4
4
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.
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