1
GATE CSE 2014 Set 1
+1
-0.3
Which one of the following is TRUE?
A
The language $$L = \left\{ {{a^n}\,{b^n}\left| {n \ge 0} \right.} \right\}$$ is regular.
B
The language $$L = \,\,\left\{ {{a^n}\,\left| n \right.\,} \right.$$ is prime$$\left. \, \right\}$$ is regular.
C
The language $$L = \left\{ {w\left| {w\,\,} \right.} \right.$$ has $$3k+1$$ $$b'$$ $$s$$ for some $$k \in N$$ with $$\sum { = \left\{ {a,\,\,b} \right\}\left. \, \right\}}$$ is regular.
D
The language $$L = \left\{ {ww\,\left| {w \in \sum {{}^ * } } \right.} \right.$$ with $$\sum { = \left. {\left\{ {0,\,\,1} \right\}} \right\}}$$ is regular.
2
GATE CSE 2014 Set 1
+1
-0.3
Consider the finite automation in the following figure.

What is the set of reachable states for the input string $$0011?$$

A
$$\left\{ {{q_0},\,{q_1},\,{q_2}} \right\}$$
B
$$\left\{ {{q_0},\,{q_1}} \right\}$$
C
$$\left\{ {{q_0},\,{q_1},\,{q_2},\,{q_3}} \right\}$$
D
$$\left\{ {{q_3}} \right\}$$
3
GATE CSE 2013
+1
-0.3
Consider the languages $${L_1} = \phi$$ and $${L_2} = \left\{ a \right\}.$$ Which one of the following represents $${L_1}\,L_2^ * UL_1^ * ?$$
A
$$\left\{ \varepsilon \right\}$$
B
$$\phi$$
C
$${a^ * }$$
D
$$\left\{ {\varepsilon ,a} \right\}$$
4
GATE CSE 2012
+1
-0.3
What is the complement of the language accepted by the $$NFA$$ shown below?
Assume $$\sum { = \left\{ a \right\}\,\,}$$ and $$\varepsilon$$ is the empty string.
A
$$\phi$$
B
$$\left\{ \varepsilon \right\}$$
C
$$a{}^ *$$
D
$$\left\{ {a,\,\,\varepsilon } \right\}$$
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