1

GATE CSE 2020

Numerical

+2

-0.67

Consider the following language.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.

Your input ____

2

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?

3

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 ____

4

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**?

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)
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