How (a*b*)* generates 'ba' substring.

Question

In Regular Expressions I saw

(a+b)* = (a*b*)*

Now my question is how (a*b*)* is able to generate 'ba' string (or any string in which 'a' comes after 'b')

Comments

First of all the significance of Kleene's operator should be known to u..

(a*b*)* means  any number of (a*b*) in succession..So out of a*b* , we can extract either 'a' or 'b' in each of a*b*..

So for string "ba" , take 'b' out of first a*b* then a out of second a*b*..

Answer 1

(a*b*)* means that to we can take 'a' any number of times, then we can take 'b' any number of times, and then we can keep repeating this process any number of times. Here 'any number of times' also includes zero times.

Here is how one can generate the required string:

$(a^{*}b^{*})^{*} \rightarrow (a^{*}b^{*})^{2} \rightarrow  (a^{*}b^{*})(a^{*}b^{*}) \rightarrow  (a^{0}b^{1})(a^{1}b^{0}) \rightarrow  (b)(a) \rightarrow  ba$.

:)

Comments

That's what I was looking for!

Thanks!

:)