Hi James,
Interesting, as I make a similar argument. I'm using an unconventional model of universal computation on finite state machinery that, among other
and from your other email,
There is still a halting problem, just not a practical halting problem for most intents and purposes.
As the units of computation in your model are finite state machines the halting problem doesn't exist in theory either. Whether or not it exists in practice depends on the dynamics you use, i.e. you could still have a very large state space where for practical purposes it was impossible to tell if an algorithm was going to halt. However by the sounds of it your dynamics limit such behaviour long before this becomes an issue. All of which raises an important point: People often assume that the best theoretical model to use when thinking about AI is the TM. However TMs are of course impossible (given current physics) and any real AI is going to have to be (technically) a finite state autonomaton, all be it one with a very large state space. This could turn out to be important as it is often the case that with weaker models of computation you are able to prove stronger results about a system's behaviour (for example whether the system halts on all inputs or if two systems recognise the same language). Nevertheless (getting back to the original topic) I don't think that Pei's model can be more powerful than a TM as he claims. What I'm saying above is that being *less* powerful than a TM does have some advantages from an analysis point of view.
I doubt that your model is really all that fundamentally different.We implement a virtual machine on top of a standard computer architecture that is designed around a fundamentally different model of a universal computer.
Either your model isn't a truly universal computer as you claim, or
your universal computer is in fact equivalent to the UTM model in
which case I wouldn't describe it as being fundamentally different.
I suspect that the former is the case: that you weren't using the
phrase "universal computer" in the technical sense of meaning a machine
which is able to perfectly emulate any other well defined machine.
Indeed if your model of computation limits unbounded recursion then
this would necessiarly be the case as any algorithm that required
a sufficient depth of recursion wouldn't be computable within your
model.
Of course the really important question is: Does any of this matter?
And the answer to that question could well be "no".
Cheers
Shane
-------
To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
