Regular Expression

Question

Given statement is true or false 

1. L is regular language $\Leftrightarrow$ Ǝ a regular expression without $\bigstar$ 

answer in detail 

Answer 1

TRUE

L is regular language ⇔Ǝ a regular expression . //original expression

But

a regular expression with *  => regular expression without * // Informally

(you can take null for example)

Comments

not getting ... and given ans is false

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i mean to say is we can write regular expression,for a regular language.

NOw, if we write a regular expression ...like (a+b)*, then we also can derive NULL from (a+b)*.

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whatever you wrote now i got ...but still m not getting whats mean of statement and why it is false

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See if a language is regular,we can write reg exp,

now suppose we wrote one.................... like      ab // it do not contain any *

now we write another one ....................... like      (ab)* // It contain * but it also can be written without * .i.e NULL

BOTH cases ,can be written without *

Answer 2

As far as I think there is also the base case that is..
1.phi
2._€
3._a
And other are
4.R1+R2
5.R1.R2
6.R1*

SO BASE CASE IS NECESSARY 1,2,3 IF FRM 4,5,6 ANY ONE IS FULFILLED ITS REGULAR EXPRESSION..
SOURCE -NPTEL VIDEO

Answer 3

i think this statement is only one way true it is not a bidirectional statement L is a regular language it does not necessary imply that there exists a regular expression without kleen star but if a regular expression exist without kleen star it means it is finite so necessarily would be regular language therefore all over it is false statement