1
GATE CSE 2016 Set 2
Numerical
+1
-0
The number of states in the minimum sized $$DFA$$ that accepts the language defined by the regular expression $${\left( {0 + 1} \right)^ * }\left( {0 + 1} \right){\left( {0 + 1} \right)^ * }$$\$
is ___________________.
2
GATE CSE 2016 Set 2
+1
-0.3
Language $${L_1}$$ is defined by the grammar: $$S{}_1 \to a{S_1}b|\varepsilon$$
Language $${L_2}$$ is defined by the grammar: $$S{}_2 \to ab{S_2}|\varepsilon$$

Consider the following statements:
$$P:$$ $${L_1}$$ is regular
$$Q:$$ $${L_2}$$ is regular

Which one of the following is TRUE?

A
Both $$P$$ and $$Q$$ are true
B
$$P$$ is true and $$Q$$ is false
C
$$P$$ is false and $$Q$$ is true
D
Both $$P$$ and $$Q$$ are false
3
GATE CSE 2016 Set 2
+1
-0.3
Consider the following types of languages: $${L_1}:$$ Regular, $${L_2}:$$ Context-free, $${L_3}:$$ Recursive, $${L_4}:$$ Recursively enumerable. Which of the following is/are TRUE?

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\overline {{L_3}} \cup {L_4}$$ is recursively enumerable
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ $$\overline {{L_2}} \cup {L_3}$$ is recursive
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ $$L_1^ * \cap {L_2}$$ is context-free
$$\,\,\,{\rm I}V.\,\,\,\,\,\,\,$$ $${L_1} \cup \overline {{L_2}}$$ is context-free

A
$${\rm I}$$ only
B
$${\rm I}$$ and $${\rm III}$$ only
C
$${\rm I}$$ and $${\rm IV}$$ only
D
$${\rm I},$$ $${\rm II}$$ and $${\rm III}$$ only
4
GATE CSE 2016 Set 2
+2
-0.6
Consider the following two statements:

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$NFA$$ is $$\sum {^ * } .$$
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ There exists a regular language $$A$$ such that for all languages $$B,A \cap B$$ is
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ regular.

Which one of the following is CORRECT?

A
Only $${\rm I}$$ is true
B
Only $${\rm II}$$ is true
C
Both $${\rm I}$$ and $${\rm II}$$ are true
D
Both $${\rm I}$$ and $${\rm II}$$ are false
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