I'm currently working on the following problem for my computer theory class. It goes as follows:
Let $A$ and $B$ be regular expressions. Show then that $A^* B$ is the solution of $X = AX + B$.
Am I supposed to let $X = A^*B$? If so then
$$A^* B = A(A^* B) + B$$
I can understand that $A(A^* B)$ could be reduced to $A^*B$ but what happens with the ${}+ B$ part of the expression?
I've read up on Kleene algebra and found an axiom that seems relevant in which
$$b + ax \leq x \Rightarrow a^∗b \leq x $$
but I'm not actually sure if it applies.
