1
GATE CSE 2001
+1
-0.3
Consider the following two statements;
$${S_1}\,\,:\,\,\left\{ {{0^{2n}}\left| {n \ge 1} \right.} \right\}$$ is a regular language
$${S_2}\,\,:\,\,\left\{ {{0^m}{1^n}{0^{m + n}}\left| {m \ge 1} \right.\,\,and\,\,n \ge \left. 1 \right\}} \right.$$ is a regular language

Which of the following statements is correct?

A
Only $${S_1}$$ is correct
B
Only $${S_2}$$ is correct
C
Both $${S_1}$$ and $${S_2}$$ are correct
D
None of $${S_1}$$ and $${S_2}$$ is correct
2
GATE CSE 2001
+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
$$N!$$
3
GATE CSE 2000
+1
-0.3
Let $$S$$ and $$T$$ be languages over $$\sum { = \left\{ {a,b} \right\}}$$ represented by the regular expressions $${\left( {a + {b^ * }} \right)^ * }$$ and $$\,{\left( {a + b} \right)^ * },$$ respectively. Which of the following is true?
A
$$S \subset T$$
B
$$T \subset S$$
C
$$S=T$$
D
$$S \cap T = \phi$$
4
GATE CSE 2000
+1
-0.3
Let $$L$$ denote the language generated by the grammar $$S \to 0S\left. 0 \right|00.$$ Which one of the following is true?
A
$$L = {0^ + }$$
B
$$L$$ is regular but not $${0^ + }$$
C
$$L$$ is context free but not regular
D
$$L$$ is not context free
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