It depends on what you combine the state machine with. State machine + sequential read of a tape = "fsm", regular languages State machine + sequential read of

It depends on what you combine the state machine with. State machine + sequential read of a tape = "fsm", regular languages State machine + sequential read of a tape + stack = "pda" push down automaton aka stack machine, context free languages State machine + arbitrary read of a tape + memory tape = Turing machine, do anything But still the state machine is finite.