Wouldn't a DFA for a computer have to have 2^n states for n bits of memory, so it's size would be exponential to memory size of the computer? So even for a pede

Wouldn't a DFA for a computer have to have 2^n states for n bits of memory, so it's size would be exponential to memory size of the computer? So even for a pedestrian 640K of memory, that's like 10^10^7 states. Sounds a lot like trying to simulate a non-deterministic Turing machine on a deterministic machine; the state space explodes exponentially making it intractable.