GATE CSE 1992 | Finite Automata and Regular Language Question 108 | Theory of Computation

GATE CSE 1992

MCQ (Single Correct Answer)

-0.6

Which of the following regular expression identities are true?

$$r\left( {^ * } \right) = r{}^ * $$

$$\left( {r{}^ * s{}^ * } \right){}^ * = \left( {r + s} \right){}^ * $$

$$\,\left( {r + s} \right){}^ * = r{}^ * + s{}^ * $$

$$r{}^ * s{}^ * = r{}^ * + s{}^ * $$

GATE CSE 1991

MCQ (Single Correct Answer)

-0.6

Let $$r = 1\,{\left( {1 + 0} \right)^ * },s = {11^ * }\,0$$ and $$\,t = {1^ * }\,0$$ be three regular expressions. Which one of the following is true?

$$L\left( s \right) \subseteq L\left( r \right)\,\,$$ and $$L\left( s \right) \subseteq L\left( t \right)\,\,$$

$$L\left( r \right) \subseteq L\left( s \right)\,\,$$ and $$L\left( s \right) \subseteq L\left( t \right)\,\,$$

$$L\left( s \right) \subseteq L\left( t \right)\,\,$$ and $$L\left( s \right) \subseteq L\left( r \right)\,\,$$

$$L\left( t \right) \subseteq L\left( s \right)\,\,$$ and $$L\left( s \right) \subseteq L\left( r \right)\,\,$$

GATE CSE 1990

MCQ (Single Correct Answer)

-0.6

Let $${R_1}$$ and $${R_2}$$ be regular sets defined over the alphabet $$\sum \, $$ then:

$${R_1} \cap R{}_2$$ is not regular.

$${R_1} \cup R{}_2$$ is regular.

$$\sum {^{^ * }} $$ $$-$$ $${R_1}$$ is regular.

$${R_1}{}^ * $$ is not regular.

GATE CSE 1989

Subjective

-0

How many substrings (of all lengths inclusive ) can be formed from a character string of length $$n$$? Assume all characters to be distinct. Prove your answer.