1
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.
2
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 $$1$$
3
GATE CSE 2003
+1
-0.3
The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ *$$denotes the same set as
A
$$\left( {{1^ * }0} \right){}^ * {1^ * }$$
B
$$0 + \left( {0 + 10} \right){}^ *$$
C
$$\left( {0 + 1} \right){}^ * 10\left( {0 + 1} \right){}^ *$$
D
None of the above.
4
GATE CSE 2003
+1
-0.3
Consider the set $$\sum {^ * }$$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } }$$ with the concatenation operator for strings
A
Does not from a group
B
Forms a non-commutative group
C
Does not have a right identity element
D
Forms a group if the empty string is removed from $${\sum {^ * } }$$
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