1
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
$$\left\{ {\varepsilon ,a} \right\}$$
2
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
$$\left\{ {a,\,\,\varepsilon } \right\}$$
3
GATE CSE 2010
+1
-0.3
Let $${L_1}$$ recursive language. Let $${L_2}$$ and $${L_3}$$ be languages that are recursively enumerable but not recursive. Which of the following statement is not necessarily true?
A
$${L_2}$$ $$-$$ $${L_1}$$ is recursively enumerable.
B
$${L_1}$$ $$-$$ $${L_3}$$ recursively enumerable.
C
$${L_2} \cap {L_1}$$ is recursively enumerable.
D
$${L_2} \cup {L_1}$$ is recursively enumerable.
4
GATE CSE 2009
+1
-0.3
Which one of the following languages over the alphabet $$\left\{ {0,\left. 1 \right)} \right.$$ is described by the regular expression $${\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }$$
A
The set of all strings containing the substring $$00$$
B
The set of all strings containing at most two $$0’$$s
C
The set of all strings containing at least two $$0’$$s
D
The set of all strings that begin and end with either $$0$$ or $$1$$
GATE CSE Subjects
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