1

GATE CSE 2018

MCQ (Single Correct Answer)

+2

-0.6

Let $$N$$ be an $$NFA$$ with $$n$$ states. Let $$k$$ be the number of states of a minimal $$DFA$$ which is equivalent to $$N.$$ Which one of the following is necessarily true?

2

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 ____

3

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**?

4

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**?

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

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2021 Set 1 (1)
GATE CSE 2020 (1)
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GATE CSE 2016 Set 2 (2)
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GATE CSE 1991 (1)
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GATE CSE 1989 (1)

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