The connection between regular languages and formal power series

51 Views Asked by At

Is there a characterization of the regular languages involving formal power series? I saw $\frac{1}{1-x} = 1+x+x^2+x^3+\cdots$ and $A^* = \epsilon + A + AA + AAA + \cdots$ in two different contexts on the same day and it made me curious if there was yet another characterization of the regular languages I didn't know about.