What will be the R.E of this DFA

Question

I'm getting (a+ba*b)*a*b

Comments

May you guys do the reverse, please, can you please show from R.E -(a + ba*b)*ba* to make FA w/ steps?

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yes order matters a lot bcz  in RE operations here  "." operator  represents  concatination

so while concatinating a string we should follow the crt order .

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by using the resolution method ..!

(a + ba*b)* ba*

Answer 1

There are 2 approaches :

A) Reaching to final state B and then considering the loops on it..

In that case to reach state B we need : a*b.

And then incoming loops are because of 'a' and 'ba*b'..

So regular expression formed this way  =  a*b ( a + ba*b )*

B) Imagining A to be a final state considering loops on it and then reaching state B 

In that case incoming loops on A are 'a' and 'ba*b'...

And then we reach B using : ba*..

So regular expression formed this way : (a + ba*b)* ba*..

The earlier approach is known as right resolution and later approach is known as left resolution..

Hence both regular expressions are equivalent...

In fact the property  = > P(QP)*  = (PQ)* P follows from this approach only.. 

Comments

What if we have multiple final states? How should we loop in that case?

Any reference for this method. The method I know is "state elimination method".