1
GATE CSE 2018
+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?
A
$$k \ge {2^n}$$
B
$$k \ge n$$
C
$$k \le {n^2}$$
D
$$k \le {2^n}$$
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 $$i > 0$$

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 _____.

3
GATE CSE 2016 Set 2
+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?

A
Only $${\rm I}$$ is true
B
Only $${\rm II}$$ is true
C
Both $${\rm I}$$ and $${\rm II}$$ are true
D
Both $${\rm I}$$ and $${\rm II}$$ are false
4
GATE CSE 2016 Set 2
+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?

A
Both $${L_1}$$ and $${L_2}$$ are context-free.
B
$${L_1}$$ is context-free while $${L_2}$$ is not context-free.
C
$${L_2}$$ is context-free while $${L_1}$$ is not context-free.
D
Neither $${L_1}$$ nor $${L_2}$$ is context-free.
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
EXAM MAP
Joint Entrance Examination