Find Regular Expression by Arden’s Theorem:


Calculate RE of this machine by Arden’s Theorem:



First we calculate all the state. 


Starting state q1 accept λ and we can also get q1 by q1.b or q2.a


Now we can get q2 by q2.b or q1.a


Now if apply Arden’s theorem to q2 then


q2 = (q1a)b* as per Arden’s theorem where r = q2, p = b and q = q1.a


Here q1 is the final state, then write q1 equation and solve as per Arden’s theorem.


Now we can write above equation as r = q + rp = qp* to apply Arden’s theorem.

We can say r = q1, p = (b + ab*a) and q = λ. 


Then as per Arden’s theorem we can write, 


Regular Expression RE = (b + a*ba)*