1

GATE CSE 2018

Numerical

+2

-0

Given a language $$𝐿,$$ define $${L^i}$$ as follows: $${L^0} = \left\{ \varepsilon \right\}$$

$${L^i} = {L^{i - 1}}.\,\,L$$ for all $$i > 0$$

$${L^i} = {L^{i - 1}}.\,\,L$$ for all $$i > 0$$

The order of a language $$L$$ is defined as the smallest k such that $${L^k} = {L^{k + 1}}.$$ Consider the language $${L_1}$$ (over alphabet $$0$$) accepted by the following automaton.

The order of $${L_1}$$ is _____.

Your input ____

2

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Consider the following two statements:

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$NFA$$ is $$\sum {^ * } .$$

$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ There exists a regular language $$A$$ such that for all languages $$B,A \cap B$$ is

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ regular.

Which one of the following is **CORRECT**?

3

GATE CSE 2016 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Consider the following languages:
$$$\eqalign{
& {L_1} = \left\{ {{a^n}{b^m}{c^{n + m}}:m,n \ge 1} \right\} \cr
& {L_2} = \left\{ {{a^n}{b^n}{c^{2n}}:n \ge 1} \right\} \cr} $$$

Which one of the following is **TRUE**?

4

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Consider the transition diagram of a $$PDA$$ given below with input alphabet $$\sum {\, = \left\{ {a,b} \right\}} $$ and stack alphabet $$\Gamma = \left\{ {X,Z} \right\}.$$ $$Z$$ is the initial stack symbol. Let $$L$$ denote the language accepted by the $$PDA.$$

Which one of the following is **TRUE**?

Questions Asked from Finite Automata and Regular Language (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2023 (1)
GATE CSE 2021 Set 1 (1)
GATE CSE 2020 (1)
GATE CSE 2018 (2)
GATE CSE 2016 Set 2 (2)
GATE CSE 2016 Set 1 (1)
GATE CSE 2015 Set 2 (3)
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GATE CSE 2014 Set 1 (1)
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GATE CSE 2008 (3)
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GATE CSE 2005 (1)
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GATE CSE 2003 (2)
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GATE CSE 2001 (2)
GATE CSE 2000 (1)
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GATE CSE 1997 (1)
GATE CSE 1995 (2)
GATE CSE 1994 (2)
GATE CSE 1992 (2)
GATE CSE 1991 (1)
GATE CSE 1990 (1)
GATE CSE 1989 (1)

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