I think most people wouldn't assume a discrete nature of finite state changes as I take from your comment. A cauchy series for example orbits around a limit poi

I think most people wouldn't assume a discrete nature of finite state changes as I take from your comment. A cauchy series for example orbits around a limit point. Fixed states would be enumerated by Natural numbers that are extensionally defined in set theory for example as ( 0 ), [ 1, ( 0 ) ], { 2, [ 1, ( 0 ) ] }, ... Be 0 the empty set, then this is the Von Neumann construction [1]. This is a very tangible notion that represents a total order. So a state is a sequence of inputs and the natural number represents the recursion depth of the successor funtion (succ). But the complexity of that function alone is less than NP, so it would not have arbitrary consequences, so cycles would be the least of a problem. A P-adic numbers field Q_p on the other hand isn't even well ordered. Or Pi, it contains many different fixed length versions of itself in its remainder. [1] https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_construction https://en.wikipedia.org/wiki/Natural_number#Von_Neumann_con... [2] https://en.wikipedia.org/wiki/Mealy_machine https://en.wikipedia.org/wiki/Mealy_machine