GATE CSE 2003 | Finite Automata and Regular Language Question 68 | Theory of Computation

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.

GATE CSE 2001

MCQ (Single Correct Answer)

-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

$${N^2}$$

$${2^N}$$

$$2N$$

$$N!$$

GATE CSE 2001

MCQ (Single Correct Answer)

-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?

Only $${S_1}$$ is correct

Only $${S_2}$$ is correct

Both $${S_1}$$ and $${S_2}$$ are correct

None of $${S_1}$$ and $${S_2}$$ is correct

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