GATE CSE 2010 | Finite Automata and Regular Language Question 63 | Theory of Computation

GATE CSE 2010

MCQ (Single Correct Answer)

-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?

$${L_2}$$ $$-$$ $${L_1}$$ is recursively enumerable.

$${L_1}$$ $$-$$ $${L_3}$$ recursively enumerable.

$${L_2} \cap {L_1}$$ is recursively enumerable.

$${L_2} \cup {L_1}$$ is recursively enumerable.

GATE CSE 2009

MCQ (Single Correct Answer)

-0.3

Which one of the following languages over the alphabet $$\left\{ {0,\left. 1 \right)} \right.$$ is described by the regular expression $${\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }$$

The set of all strings containing the substring $$00$$

The set of all strings containing at most two $$0’$$s

The set of all strings containing at least two $$0’$$s

The set of all strings that begin and end with either $$0$$ or $$1$$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } } $$ with the concatenation operator for strings

Does not from a group

Forms a non-commutative group

Does not have a right identity element

Forms a group if the empty string is removed from $${\sum {^ * } }$$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.3

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

$$\left( {{1^ * }0} \right){}^ * {1^ * }$$

$$0 + \left( {0 + 10} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * 10\left( {0 + 1} \right){}^ * $$

None of the above.