1
GATE CSE 2006
+2
-0.6
Consider the regular language $$L = {\left( {111 + 11111} \right)^ * }.$$ The minimum number of states in any $$DFA$$ accepting this language is
A
$$3$$
B
$$5$$
C
$$8$$
D
$$9$$
2
GATE CSE 2005
+2
-0.6
Consider the machine $$M:$$ The language recognized by $$M$$ is: A
$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ every $$a$$ in $$w$$ is followed by exactly two $$\left. {b's} \right\}$$
B
$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ every $$a$$ in $$w$$ is followed by at least two $$\left. {b's} \right\}$$
C
$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ $$w$$ contains the substring $$\,\left. {'abb'\,\,} \right\}\,$$
D
$$\left\{ {w\,\, \in \,\left\{ {a,b} \right\}{}^ * \left| \, \right.} \right.$$ $$w$$ does not contain $$'aa'$$ as a substring$$\left. \, \right\}$$
3
GATE CSE 2004
+2
-0.6
The following finite state machine accepts all those binary strings in which the number of $$1's$$ and $$0's$$ are respectively A
Divisible by $$3$$ and $$2$$
B
Odd and even
C
Even and odd
D
Divisible by $$2$$ and $$3$$
4
GATE CSE 2003
+2
-0.6
Consider the $$NFA$$ $$M$$ shown below. Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language accepted by the $$NFA$$, $${M_1}$$ obtained by changing the accepting state of $$M$$ to a non accepting state and by changing the non accepting state of $$M$$ to accepting states. Which of the following statements is true?

A
$${L_1} = \left\{ {0,\,1} \right\}{}^ * - L$$
B
$${L_1} = \left\{ {0,\,1} \right\}{}^ *$$
C
$${L_1} \subseteq \,L$$
D
$${L_1} = \,L$$
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
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