1
GATE CSE 2015 Set 1
+2
-0.6
Consider the NPDA $$\left\langle {Q = \left\{ {{q_0},{q_1},{q_2}} \right\}} \right.,$$ $$\Sigma = \left \{ 0, 1 \right \},$$ $$\Gamma = \left \{ 0, 1, \perp \right \},$$ $$\delta, q_{0}, \perp,$$ $$\left. {F = \left\{ {{q_2}} \right\}} \right\rangle$$ , where (as per usual convention) $$Q$$ is the set of states, $$\Sigma$$ is the input alphabet, $$\Gamma$$ is the stack alphabet, $$\delta$$ is the state transition function q0 is the initial state, $$\perp$$ is the initial stack symbol, and F is the set of accepting states. The state transition is as follows: Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton?

A
10110
B
10010
C
01010
D
01001
2
GATE CSE 2015 Set 2
Numerical
+2
-0
The number of states in the minimal deterministic finite automaton corresponding to the regular expression $${\left( {0 + 1} \right)^{\,\, * }}\left( {10} \right)$$ is ________________.
3
GATE CSE 2015 Set 2
+2
-0.6
Which of the following languages is/are regular?

$${L_1}:\left\{ {wx{w^R}|w,x\, \in \left\{ {a,b} \right\}{}^ * } \right.$$ and $$\left. {\left| w \right|,\left| x \right| > 0} \right\},\,{w^R}$$ is the reverse of string $$w$$
$${L_2}:\left\{ {{a^n}{b^m}\left| {m \ne n} \right.} \right.$$ and $$m,n \ge \left. 0 \right\}$$
$${L_3}:\left\{ {{a^p}{b^q}{c^r}\left| {p,q,r \ge 0} \right.} \right\}$$

A
$${L_1}$$ and $${L_3}$$ only
B
$${L_2}$$ only
C
$${L_2}$$ and $${L_3}$$ only
D
$${L_3}$$ only
4
GATE CSE 2015 Set 2
+2
-0.6
Consider the alphabet $$\sum { = \left\{ {0,1} \right\},}$$ the null/empty string $$\lambda$$ and the sets of strings $${X_0},\,{X_1},$$ and $${X_2}$$ generated by the corresponding non-terminals of a regular grammar. $${X_0},\,\,{X_1},\,$$ and $${X_2}$$ are related as follows. \eqalign{ & {X_0} = 1\,X{}_1 \cr & {X_1} = 0{X_1} + 1\,{X_2} \cr & {X_2} = 0\,{X_1} + \left\{ \lambda \right\} \cr}\$
Which one of the following choices precisely represents the strings in $${X_0}$$?
A
$$10\left( {{0^ * } + {{\left( {10} \right)}^ * }} \right)1$$
B
$$10\left( {{0^ * } + \left( {10} \right){}^ * } \right){}^ * 1$$
C
$$1\left( {0 + 10} \right){}^ * 1$$
D
$$10\left( {0 + 10} \right){}^ * 1 + 110\left( {0 + 10} \right){}^ * 1$$
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