Regular Languages

Question

The solution to $X = r +Xs$ by Arden’s Lemma when s has ϵ
a) an infinite number of solutions
b) a finite number of solutions
c) is always unique
d) none

Answer 1

if s is not epsilon it has unique solution according to ardens theorem.

but if it is epsilon.

let X=r+Xs and s=epsilon

when we apply ardens theorem X=rs* substituting s=epsilon in solution .the equ becomes X=r as epsilon power anything is epsilon.

hence it has finite solution.