A finite-state machine has \(n\) states and \(m\) possible inputs.
Each combination of state and input returns a new state.
This can be representated with an \(m\) by \(n\) matrix, or a graph.
This is similar to combinatorial logic, but the output is the new state rather than a general output.
This means that successive inputs can be given to a finite state machine, whereas for combinatorial logic only the most recent input matters.