Wow, thank you.

So I adhere to the Schützenberger view of automata theory, that the way to explain a semester's finite automata theory to a math major in twenty minutes is via rational power series on noncommuting variables. Change the semiring from true/false to probabilities and one gets hidden Markov chain theory.

So how do nondeterministic transition systems fit into this picture? I'm guessing that the connection should blow my mind with a new way to see power series?