1
GATE CSE 2014 Set 1
+2
-0.6
Which of the regular expression given below represent the following $$DFA?$$  A
$${\rm I}$$ and $${\rm II}$$ only
B
$${\rm I}$$ and $${\rm III}$$ only
C
$${\rm II}$$ and $${\rm III}$$ only
D
$${\rm I}$$, $${\rm II}$$ and $${\rm III}$$
2
GATE CSE 2013
+2
-0.6
Consider the following languages
$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is FALSE?

A
$${L_2}$$ is context-free
B
$${L_1} \cap {L_2}$$ is context-free
C
Complement of $${L_2}$$ is recursive
D
Complement of $${L_1}$$ is context-free but not regular
3
GATE CSE 2012
+2
-0.6
Consider the set of strings on $$\left\{ {0,1} \right\}$$ in which, every substring of $$3$$ symbols has at most two zeros. For example, $$001110$$ and $$011001$$ are in the language, but $$100010$$ is not. All strings of length less than $$3$$ are also in the language. A partially completed $$DFA$$ that accepts this language is shown below.

The missing arcs in the $$DFA$$ are A B C D 4
GATE CSE 2011
+2
-0.6
Definition of the language $$L$$ with alphabet $$\left\{ a \right\}$$ is given as following. $$L = \left\{ {{a^{nk}}} \right.\left| {k > 0,\,n} \right.$$ is a positive integer constant$$\left. \, \right\}$$

What is the minimum number of states needed in a $$DFA$$ to recognize $$L$$?

A
$$k+1$$
B
$$n+1$$
C
$${2^{n + 1}}$$
D
$${2^{k + 1}}$$
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