1
GATE CSE 2002
+2
-0.6
The Finite state machine described by the following state diagram with $$A$$ as starting state, where an arc label is $$x/y$$ and $$x$$ stands for $$1-bit$$ input and $$y$$ stands for $$2$$-bit output A
Outputs the sum of the present and the previous bits of the input.
B
Outputs $$01$$ whenever the input sequence contains $$11$$
C
Outputs $$00$$ whenever the input sequence contains $$10$$
D
None of the above
2
GATE CSE 2001
+2
-0.6
Consider a $$DFA$$ over $$\sum { = \left\{ {a,\,\,b} \right\}}$$ accepting all strings which have number of $$a'$$s divisible by $$6$$ and number of $$b'$$s divisible by $$8$$. What is the minimum number of states that the $$DFA$$ will have?
A
$$8$$
B
$$14$$
C
$$15$$
D
$$48$$
3
GATE CSE 2001
+2
-0.6
Consider the following languages:
$${L_1} = \left\{ {w\,w\left| {w \in {{\left\{ {a,\,b} \right\}}^ * }} \right.} \right\}$$
$${L_2} = \left\{ {w\,{w^R}\left| {w \in {{\left\{ {a,\,b} \right\}}^ * },} \right.{w^R}\,\,} \right.$$ is the reverse of $$\left. w \right\}$$
$${L_3} = \left\{ {{0^{2i}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$
$${L_4} = \left\{ {{0^{{i^2}}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$

Which of the languages are regular?

A
Only $${L_1}$$ and $${L_2}$$
B
Only $${L_2},$$ $${L_3}$$ and $${L_4}$$
C
Only $${L_3}$$ and $${L_4}$$
D
Only $${L_3}$$
4
GATE CSE 2000
+2
-0.6
What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has two states?
A
Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is odd $$\left. \, \right\}$$
B
Must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is even $$\left. \, \right\}$$
C
Must be $$\left\{ {{a^n}\left| {n \ge } \right.\,\,} \right.0\left. \, \right\}$$
D
Either $$L$$ must be $$\left\{ {{a^n}\left| n \right.\,\,} \right.$$ is odd$$\left. \, \right\}\,\,$$ or $$L$$ must be $$\left\{ {{a^n}\left| n \right.} \right.$$ is even$$\left. \, \right\}$$
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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