Neuring Machine

[Paul Kube]

   Date: Mon, 15 Jan 90 13:27:55 EST
   From: Jordan B Pollack <pollack at cis.ohio-state.edu>

   How could you get the unbounded tape INSIDE a machine? 
   For integer machines, assume unbounded registers. For cellular
   automata, assume an unbounded lattice. For connectionist models,
   assume that two units could encode the tape as binary rationals. 

Or assume an unbounded network.

   Date: Mon, 15 Jan 90 11:07:21 -0500
   From: Jim Hendler <hendler at cs.UMD.EDU>

   I'm a little confused by Dave's argument, and some of the others
   I've seen.   My Sun, built out of wires and etc. is not
   equivalent to a Turing machine, it has limited state, etc.

See above.

   To say that a Turing machine could be built from connectionist
   components is not to argue that they are formally equivalent.

Showing how you can simulate the operation of a
universal TM in another machine is usually how you show that
TM's are no more powerful than the other machine.

   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.

Why you think it's okay to suppose you have infinite-precision neurons
but not okay to suppose you have infinitely many neurons is a mystery to me,
since each seems about as impossible as the other.  

	--Paul 
	kube at cs.ucsd.edu