1
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.
2
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
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
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12