Consider the two following definitions:
Discrete Deterministic System: a system where inputs and outputs can have only a finite number of values, and is deterministic;
Finite State Machine: an abstract machine that can be in exactly one of a finite number of states at any given time.
My understanding is that the states in a discrete deterministic system will be a combination of the actual inputs (and possibly previous ones, if it is a system with memory), and therefore the number of states should be finite.
Provided that complexity is not a problem, is it be possible to build a finite state machine that models every possible discrete deterministic system?
If not, can you provide an example of a discrete deterministic system that cannot be represented as a finite state machine?