X-Message-Number: 8664
Date:  Thu, 09 Oct 97 18:53:54 
From: Mike Perry <>
Subject: TMs, NNs, QCs, many-worlds

Thomas Donaldson, #8663, wrote:

>It seems someone else doesn't like the idea of nonTuring Machine
>computers.
>
>As I understand the model set up by the two guys who proposed it, it's
>not necessary to work in infinite precision. Just work in arbitrarily
>large precision. So you work with long sequences of integers. 
>
>In a real device you can do even more. The claim of the paper was that

Somehow I missed the reference you are citing--didn't find it in my 
message files. Can you tell me what it is? Thanks.

Also, anyone, I'm looking for some 
information on the quantum encryption 
channel. Supposedly its absolutely secure, yet I've heard an argument 
it isn't because errors could be surreptitiously introduced from the 
outside (I think). This (the secure channel) is cited by David
Deutsch in his recent book *The Fabric of Reality* as a type of
device a Turing machine could not duplicate (or emulate?). I don't
see how though--even if it works perfectly, a TM ought at least
to be able to model a region of spacetime in which such a device is
operating, along with sender and receiver. Similarly I don't see how
a neural net could not be emulated by a TM, in theory at least, as one
more finite system in our quantum universe; this should apply to 
any physically realizable connection strengths.
But comments/references appreciated.

Deutsch, by the way, makes a big appeal in his book for the many-worlds 
interpretation/formulation of things. It is, he says, really by far 
the best explanation of what is going on at the quantum level; others 
remind him of the geocentric solar system, even if they do make 
correct predictions.

Deutsch is one of the important researchers on the quantum computer. 
Although he claims the QC is more powerful, computationally, than a 
TM, as far as I can see it isn't, as long as we ignore efficiency 
considerations. If we do take efficiency into account the powers of 
the QC appear to be intermediate between the deterministic and the 
nondeterministic TM, based on material I have found on the Web. 
Again, comments/references would be appreciated (I'll supply 
references I have to anyone interested).

Mike Perry

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