Turing machines are kind of the limit of finite state machines. There are particular Turing machines that can simulate all possible finite state machines. In general, an arbitrary sequence of finite state machines can be uncomputable. But there are particular primitive recursive functions that simulate arbitrary finite state machines, (given the value as an input. ) You don’t need the full strength of turing completeness to do that. So I would say, kind of no. There are systems strictly stronger than all finite automaton, yet not Turing complete.
Really, the notion of a limit isn’t rigorously defined here, so its hard to say.
Turing machines are kind of the limit of finite state machines. There are particular Turing machines that can simulate all possible finite state machines. In general, an arbitrary sequence of finite state machines can be uncomputable. But there are particular primitive recursive functions that simulate arbitrary finite state machines, (given the value as an input. ) You don’t need the full strength of turing completeness to do that. So I would say, kind of no. There are systems strictly stronger than all finite automaton, yet not Turing complete.
Really, the notion of a limit isn’t rigorously defined here, so its hard to say.