Doubt on Kleene Closure on RE

Question

Hi Experts,

Can anyone please tell me the strings present in regular expression (ab*)*

My doubt is whether (ab*)* can have any combination of the strings in RE ab* like in the following language.

L={a,ab,abb}* = {aab,aabb,abba,ababb,..}

Here abba is obtained by combining abb and a.

Please tell me whether my understanding is right.

Thanks in advance,

VIshnu

Answer 1

(ab*)*
L=(epsilon,a,aa,aaaa,ab,abb,abab,abbbbbbbab,.......)
from outer closure u can get any no of times ab*.....from here u can get any number of b with one a...or even any number of a if we make inner b* as epsilon each time and take outer closure into consideration..

Comments

I got the ab* part.What I wanted to know was how do we apply kleene closure to ab*.

ab* = {€,a,ab,abb,..}

Can you please tell me how to apply kleene closure to ab*.i.e.the outer kleene closure.

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suppose if it would have been only (ab)*....then what could be the language...epsilon,ab,abab,ababab....so on

now just put closure on every b....thats it....
any more doubt brother?

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see this u will get the bigger picture

ab*,ab*ab*,ab*ab*ab*,.....

now try to expand each one
say ab*=a,ab,abb,abbbbb...
ab*ab*=aa,aba,abab,abba,...

this way u can do

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language starting with a and ending with a or b (including epsilon), right??