1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Which of the following languages is regular?
A
$$\left\{ {w{w^R}} \right.\left| {w \in \left\{ {0,\,1} \right\}\left. {^ + } \right\}} \right.$$
B
$$\left\{ {w{w^R}} \right.x\left| {x,w \in \left\{ {0,\,1} \right\}\left. {^ + } \right\}} \right.$$
C
$$\left\{ {wx{w^R}} \right.\left| {x,w \in \left\{ {0,\,1} \right\}\left. {^ + } \right\}} \right.$$
D
$$\left\{ {xw{w^R}} \right.\left| {x,w \in \left\{ {0,\,1} \right\}\left. {^ + } \right\}} \right.$$
2
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the following finite state automation

The language accepted by this automation is given by the regular expression

A
$${b^ * }a{b^ * }a{b^ * }a{b^ * }$$
B
$${\left( {a + b} \right)^ * }$$
C
$${b^ * }a{\left( {a + b} \right)^ * }$$
D
$${b^ * }a{b^ * }a{b^ * }$$
3
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the following finite state automation

The minimum state automation equivalent to the above $$FSA$$ has the following number of states

A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
If $$s$$ is a string over $${\left( {0 + 1} \right)^ * }$$ then let $${n_0}\left( s \right)$$ denote the number of $$0'$$ s in $$s$$ and $${n_1}\left( s \right)$$ the number of $$1'$$s in $$s.$$ Which one of the following languages is not regular?
A
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {{n_0}\left( s \right)\,\,} \right.} \right.$$ is a $$3$$-digit prime$$\left. \, \right\}$$
B
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,\,} \right.} \right.$$ for every prefix $$s'$$ of $$s.$$ $$\,\left| {{n_0}\left( {{s^,}} \right) - {n_1}\left( {{s^,}} \right)\left| { \le \left. 2 \right\}} \right.} \right.$$
C
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^*}\left\| {{n_0}\left( s \right) - {n_1}\left( s \right)\left| { \le \left. 4 \right\}} \right.} \right.} \right.$$
D
$$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }} \right.\left| {{n_0}\left( s \right)} \right.$$ mod $$7 = {n_1}\left( s \right)$$ mod $$5 = \left. 0 \right\}$$
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