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Find regular expression of the given machine

 

 

In this machine there is two final state q1 and q2. So as we know there are sum of two regular expression.

 

Regular expression of q1 = b*a(b + ba*b)* (taking longest path)

Regular expression of q2 = b*a(b + ba*b)*ba* (taking longest path)

 

Final Regular Expression:

b*a(b + ba*b)* + b*a(b + ba*b)*ba* = b*a(b + ba*b)* (λ + ba*)