Any circuit that keeps track of the current state is in effect a counter. It may not be a binary counter, but it is still a counter.And, you don't really need a physical counter, per se. You could build a synchronous state machine using just logic.
That's why I prefaced the word "counter" with the word "physical". But, thanks for the clarification.Any circuit that keeps track of the current state is in effect a counter. It may not be a binary counter, but it is still a counter.
Semantics.Any collection of memory devices (aka flip-flops) is in effect a state counter. I don't have any clue about what a non-physical counter would look like.