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[Jim Hendler]

I'm a little confused by Dave's argument, and some of the others
I've seen.  There is a difference (and a formal one) between 
performing computation and being Turing equivalent.  It is easily
done (and has been in the past) to build a small general purpose
computer out of tinkertoys (a tinkertoy computer was on display in
the computer museum in Boston for a while -- pretty limited, but a
computer none the less).  Does this mean that tinkertoys are
Turing complete?  My Sun, built out of wires and etc. is also not
equivalent to a Turing machine, it has limited state, etc.  There are
very definitely Turing computable functions that my  Sun can't compute.
To say that a Turing machine could be built from connectionist
components is not to argue that they are formally equivalent.
 The only demonstration of equivalence I've seen is the result 
Dave cites from Jordan Pollack (see his thesis) in which he shows a
reduction of a Turing machien to a particular connectionist network (given
infinite precision integers).  This is not a "simulation" of a TM, but
rather a full-fledged reduction.
 So Dave is only "almost" right (I suspect just using language loosely),
the question is whether connectionist networks with particular
architectures are Turing equivalents -- in the formal sense (not whether
they "simulate" a TM in the weaker sense that tinkertoys do).
 Anyone know of any proofs of this class?  (Note, it is important to
recognize that any such thing must be able to represent the arbitrarily
large tape of the Turing machine)
 -Jim Hendler