Pedantry: are you using "finite state machine" as a stand-in for "abstract machine"? If so, OK, otherwise, if you mean it in the sense of a Finite State Automat

Pedantry: are you using "finite state machine" as a stand-in for "abstract machine"? If so, OK, otherwise, if you mean it in the sense of a Finite State Automaton (FSA), digital computers of the kind we all use nowadays are Turing machines (with finite tapes). If digital computers were FSAs there would be a good many things you wouldn't be able to do with them, e.g. sorting a list (because that's a context-sensitive task).