1

GATE CSE 2020

MCQ (Single Correct Answer)

+2

-0.67

Which of the following languages are undecidable? Note that $$\langle M\rangle $$ indicates encoding of the Turing machine M.

L

L

L

L

L

_{1}= $$\left\{ {\langle M\rangle |L\left( M \right) = \phi } \right\}$$L

_{2}= $$\{ \langle M,w,q\rangle |$$ M on input w reaches state q in exactly 100 steps }L

_{3}= { $$\langle M\rangle |$$ L(M) is not recursive }L

_{4}= { $$\langle M\rangle |$$ L(M) contains at least 21 members }2

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible to $${L_2}$$ , which in turn is polynomial time reducible to language $${L_4}$$ . Which of the following is/are true?

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_2} \in P$$

$$\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P$$ or $$\,\,\,{L_3} \in P,$$ then $$\,\,\,{L_2} \in P$$

$$\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P,$$ and only $$\,\,\,{L_3} \in P$$

$$\,\,\,\,\,\,\,\,\,\,{\rm I}V.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_1} \in P$$ and $$\,\,\,{L_3} \in P$$

3

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Which one of the following problems is un-decidable?

4

GATE CSE 2013

MCQ (Single Correct Answer)

+2

-0.6

Which of the following is/are undecidable?

$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$

$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \sum {{}^ * } ?$$

$$3.$$ $$M$$ is a Turing Machine. Is $$L(M)$$ regular?

$$4.$$ $$A$$ is a $$DFA$$ and $$N$$ is an $$NFA.$$

Is $$L(A)=L(N)?$$

$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$

$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \sum {{}^ * } ?$$

$$3.$$ $$M$$ is a Turing Machine. Is $$L(M)$$ regular?

$$4.$$ $$A$$ is a $$DFA$$ and $$N$$ is an $$NFA.$$

Is $$L(A)=L(N)?$$

Questions Asked from Undecidability (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE Subjects

Theory of Computation

Operating Systems

Algorithms

Database Management System

Data Structures

Computer Networks

Software Engineering

Compiler Design

Web Technologies

General Aptitude

Discrete Mathematics

Programming Languages