GATE CSE 1998 | Finite Automata and Regular Language Question 83 | Theory of Computation

GATE CSE 1998

MCQ (Single Correct Answer)

-0.3

If the regular set $$A$$ is represented by $$A = {\left( {01 + 1} \right)^ * }$$ and the regular set $$'B'$$ is represented by $$B = \left( {{{\left( {01} \right)}^ * }{1^ * }} \right),$$ which of the following is true?

$$A \subset B$$

$$B \subset A$$

$$A$$ and $$B$$ are incomparable

$$A=B$$

GATE CSE 1997

MCQ (Single Correct Answer)

-0.3

$$\sum { = \left\{ {a,b} \right\},\,\,} $$ which one of the following sets is not countable.

Set of all strings over $$\sum {} $$

Set of all languages over $$\sum {} $$

Set of all regular languages over $$\sum {} $$

Set of all languages over $$\sum {} $$ accepted by Turing Machines.

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Which two of the following four regular expressions are equivalent?
(i) $${\left( {00} \right)^ * }\left( {\varepsilon + 0} \right)$$
(ii) $${\left( {00} \right)^ * }$$
(iii) $${0^ * }$$
(iv) $$0\,\,{\left( {00} \right)^ * }$$

(i) and (ii)

(ii) and (iii)

(i) and (iii)

(iii) and (vi)

GATE CSE 1996

MCQ (Single Correct Answer)

-0.3

Let $$L \subseteq \sum {^{^ * }\,} $$ where $$\,\sum { = \,\,\left\{ {a,b} \right\}\,\,} $$ which of the following is true?

$$L = \,\,\,\left\{ {\left. x \right|\,\,\,x} \right.$$ has an equal number of $$a's$$ and $$\,\left. {b's} \right\}$$ is regular

$$L = \left\{ {{a^n}{b^n}\left| {n \ge 1} \right.} \right\}$$ is regular

$$L = \,\,\,\left\{ {\left. x \right|\,\,\,x} \right.\,$$ has more $$a's$$ than $$\left. {b's} \right\}$$ is regular

$$L = \left\{ {{a^m}{b^n}\left| {m \ge 1,\,n \ge 1} \right.} \right\}$$ is regular