1

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

+1

-0.3

For any two languages L_{1} and L_{2} such that L_{1} is context-free and L_{2} is recursively enumerable but not recursive, which of the following is/are necessarily true?

_{1}) is recursive

II. $${\overline L _2}$$ (complement of L

_{2}) is recursive

III. $${\overline L _1}$$ is context-free

IV. $${\overline L _1} \cup {L_2}$$ is recursively enumerable

2

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

+1

-0.3

Consider the following statements.

$$\,\,\,$$ $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The complement of every Turing decidable language is Turing decidable

$$\,$$ $${\rm II}.\,\,\,\,\,\,\,\,\,$$ There exists some language which is in $$NP$$ but is not Turing decidable

$${\rm III}.\,\,\,\,\,\,\,\,\,$$ If $$L$$ is a language in $$NP,$$ $$L$$ is Turing decidable

Which of the above statements is/are true?

3

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

+1

-0.3

Let $$A\,\,{ \le _m}\,\,B$$ denotes that language $$A$$ is mapping reducible (also known as many-to-one reducible) to language $$B.$$ Which one of the following is FALSE?

4

GATE CSE 2013

MCQ (Single Correct Answer)

+1

-0.3

Which of the following statements is/are

$$1.$$ For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine

$$2.$$ Turing recognizable languages are closed under union and complementation

$$3.$$ Turing decidable languages are closed under intersection and complementation

$$4.$$ Turing recognizable languages are closed under union and intersection

**FALSE**?$$1.$$ For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine

$$2.$$ Turing recognizable languages are closed under union and complementation

$$3.$$ Turing decidable languages are closed under intersection and complementation

$$4.$$ Turing recognizable languages are closed under union and intersection

Questions Asked from Recursively Enumerable Language and Turing Machine (Marks 1)

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