Grammars - RegEx

I am trying to construct a regular expression that the total number of a's is divisible by 3 no matter how they are distributed. aabaabbaba. This is What i came up with:

b*ab*ab*

Now, someone told me i could do it this way

(b*ab*ab*)*

Why would i need to enclose it and why is the outside kleene star needed?

Wouldnt the outside kleene distribute among all the a's a开发者_Python百科nd b's inside the parenthesis? if thats the case then what would a double kleene mean?

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For the number of 'a's to be divisible by three, you'll need three 'a's in your expression. So the correct expression is:

(b*ab*ab*ab*)*

This expression is saying 'a' three times, with possible 'b's in the middle. The last star says repeat (the whole parenthesized expression) as necessary.

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The outer * repeats the entire sequence zero or more times.

In other words, zero or more substrings that match b*ab*ab*.