I. Using State Elimination
FA given :
Remove State B
Removing State C
Simplify it
Regular expression is (01+10)(11+1(01+10))*
II. Using Arden's Theorem
A=∊ + D0 ------- I
B= A0+D1 -------II
C=A1 -----------III
D=B1+C0 --------- IV
Putting II and III in IV
D= (A0+D1)1+A10
=A(01+10) +D11
Apply Arden's Theorem
D= A(01+10)(11)* - - - - - V
Put V in I
A=∊+A(01+10)(11)*0
Apply Arden's Theorem
A= ((01+10)(11)*0)* - - - - VI
Put VI in V
Regular expression, D = ((01+10)(11)*0)*(01+10)(11)*
= (01+10)(11)*(0(01+10)(11)*)* [ bcoz (pq)*p = p(qp)*]
= (01+10)(11+0(01+10))* [ bcoz p*(qp*)* = (p+q)*]