1
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Given an arbitrary non-deterministic finite automaton $$(NFA)$$ with $$N$$ states, the maximum number of states in an equivalent minimized $$DFA$$ is at least
A
$${N^2}$$
B
$${2^N}$$
C
$$2N$$
D
$$N!$$
2
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider a $$DFA$$ over $$\sum { = \left\{ {a,\,\,b} \right\}} $$ accepting all strings which have number of $$a'$$s divisible by $$6$$ and number of $$b'$$s divisible by $$8$$. What is the minimum number of states that the $$DFA$$ will have?
A
$$8$$
B
$$14$$
C
$$15$$
D
$$48$$
3
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-0.6
Consider the following languages:
$${L_1} = \left\{ {w\,w\left| {w \in {{\left\{ {a,\,b} \right\}}^ * }} \right.} \right\}$$
$${L_2} = \left\{ {w\,{w^R}\left| {w \in {{\left\{ {a,\,b} \right\}}^ * },} \right.{w^R}\,\,} \right.$$ is the reverse of $$\left. w \right\}$$
$${L_3} = \left\{ {{0^{2i}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$
$${L_4} = \left\{ {{0^{{i^2}}}\left| {i\,\,} \right.} \right.$$ is an integer$$\left. \, \right\}$$

Which of the languages are regular?

A
Only $${L_1}$$ and $${L_2}$$
B
Only $${L_2},$$ $${L_3}$$ and $${L_4}$$
C
Only $${L_3}$$ and $${L_4}$$
D
Only $${L_3}$$
4
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
Which of the following statement is true?
A
If a language is context free it can always be accepted by deterministic pushdown automation
B
The union of two context free language is context free
C
The intersection of two context free languages is context free
D
The complement of a context free language is context free
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