Virtual Gate Test Series: Theory Of Computation - Regular Languages

Question

Which one of the following languages over the alphabet ${0, 1}$ is regular$?$

$(A)$ The language of balanced parentheses where $0, 1$ are thought of as $(,)$ respectively

$(B)$ The language of palindromes, i.e., bit strings $x$ that read the same from left to right as well as right to left

($C)L = \{0m2 : 3 ≤ m\}$

$(D)$ The kleene closure $L^{*},$ where $L$ is the language in $(C)$ above

Ans is $D$ please explain$?$

Comments

https://gateoverflow.in/25670/tifr2013-b-8

This is this question.

Answer 1

If we put 1 in place of m in option C, and then take its kleene closure then we get L=0*.

Now we cannot add anything further whatever be the value of m, or whatever be the condition now.

And we know 0* is straight away regular.

Comments

Lucky sunda please explain in detail. i didn't get ur explanation

Why did u put 1 in place on M ?

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I have marked that answer wrong. We cannot put 1 as m>=3.

I earlier thought it be m <=3.

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I think none of them are regular.

Could you please confirm Lucky Sunda.