Question

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 and b’s inside the parenthesis? if thats the case then what would a double kleene mean?

Answer 1

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.