1
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
$$10\left( {0 + 10} \right){}^ * 1 + 110\left( {0 + 10} \right){}^ * 1$$
2
GATE CSE 2015 Set 1
Numerical
+2
-0 Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) ∩ L(N) is___________.

3
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
4
GATE CSE 2014 Set 2
+2
-0.6
Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?
A
$${L_1}$$ is regular but not $${L_2}$$
B
$${L_2}$$ is regular but not $${L_1}$$
C
Both $${L_1}$$ and $${L_2}$$ are regular
D
Neither $${L_1}$$ nor $${L_2}$$ are regular
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
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