1
GATE CSE 2010
+2
-0.6
Let $$L = \left\{ {w \in {{\left( {0 + 1} \right)}^ * }\left| {\,w} \right.} \right.$$ has even number of $$\,\left. {1's} \right\},$$ i.e $$L$$ is the set of all bit strings with even number of $$1's.$$ which one of rhe regular expression below represents $$L.$$
A
$$\left( {{0^ * }{{10}^ * }1} \right){}^ *$$
B
$${0^ * }\left( {{{10}^ * }{{10}^ * }} \right){}^ *$$
C
$${0^ * }\left( {{{10}^ * }1} \right){}^ * {0^ * }$$
D
$${0^ * }\,\,1\left( {{{10}^ * }1} \right){}^ * {10^ * }$$
2
GATE CSE 2010
+2
-0.6
Let $$w$$ be any string of length $$n$$ in $${\left\{ {0,1} \right\}^ * }$$. Let $$L$$ be the set of all substrings of $$w.$$ What is the minimum number of states in a non-deterministic finite automation that accepts $$L$$?
A
$$n-1$$
B
$$n$$
C
$$n+1$$
D
$${2^{n + 1}}$$
3
GATE CSE 2009
+2
-0.6
$$L = {L_1} \cap {L_2}$$ where $${L_1}$$ and $${L_2}$$ are languages defined as follows.
$${L_1} = \left\{ {{a^m}{b^m}\,c\,{a^n}{b^n}\left| {m,n \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{a^i}{b^i}{c^k}\left| {i,j,k \ge 0} \right.} \right\}$$ Then $$L$$ is
A
Not recursive
B
Regular
C
Context free but not regular
D
Recursively enumerable but not context free
4
GATE CSE 2009
+2
-0.6

The above $$DFA$$ accepts the set of all strings over $$\left\{ {0,\,\,1} \right\}$$ that

A
Begin either with $$0$$ or $$1$$
B
End with $$0$$
C
End with $$00.$$
D
Contain the substring $$00.$$
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