Made Easy Test Series | Theory Of Computation | Regular Grammar

Question

The following language regular

L*, where L={ $0^{{m}^{2}} | m\leq 3$ }

1. True
2. False

 

Answer 1

L = { e, 0, 0000, 000000000}.

L* = ( e + 0 + 0000 + 000000000)*

     = ( e + 0 + 0000 + 000000000)( e + 0 + 0000 + 000000000)( e + 0 + 0000 + 000000000)….

     = (e, 0, 00, 000, 0000, 00000,…….) {use e and 0 from each grouping to generate this}

     = 0*

Hence L is an RL.

Note: (Shorter and faster way to solve the sum as mentioned by @raja11sep)

Every finite language is regular.

Regular languages are closed under Kleene closure.

Comments

The given key is “not regular” 😪

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If I have done it correctly I think it should be RL.

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@Souvik33 it is Regular

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Nice Answer.

Every finite language is regular.

Regular languages are closed under Kleene closure.