Arden's theorem Statement −
Let P and Q be two regular expressions.
If P does not contain null string, then R = Q + RP has a unique solution that is R = QP*
R = Q + (Q + RP)P [After putting the value R = Q + RP]
= Q + QP + RPP
When we put the value of R recursively again and again, we get the following equation −
R = Q + QP + QP2 + QP3…..
R = Q (ε + P + P2 + P3 + …. )
R = QP* [As P* represents (ε + P + P2 + P3 + ….) ]