1
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___________.

2
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
3
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 ________________.
4
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
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