I understand you mean "deterministic finite-state machines" rather than "Turing machines". I meant "Turing machines with X states and a type limited to Y bits,

I understand you mean "deterministic finite-state machines" rather than "Turing machines". I meant "Turing machines with X states and a type limited to Y bits, with X + Y = N". You can, of course, cast those as Deterministic Finite State Machines, but that will require incredibly many states.