Finite state machines are equivalent to finite automaton, but non finite state machines are not. The most obvious difference is that a state machine can have i

Finite state machines are equivalent to finite automaton, but non finite state machines are not. The most obvious difference is that a state machine can have infinite transitions and infinite states. The most obvious example is a counter machine that simply keep tracks of how many events it received. Such state machines can be Turing complete, but also allow to add restrictions to limit their expressiveness https://en.m.wikipedia.org/wiki/Pushdown_automaton https://en.m.wikipedia.org/wiki/Pushdown_automaton Edit: to add more context Turing machines are essentially finite state machines with an unlimited memory attached and specific input events (the alphabet of the memory eg bits) and output states (move left/right, write, halt; with possibly multiple state for each output)