Neuring Machine

[Jordan B Pollack]

McCulloch and Pitts showed that their network could act as the finite
state control of a Turing Machine, acting upon an EXTERNAL tape.

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. 

As Dave alluded to, in my May 1987 thesis*, I showed that a Turing
Machine could be constructed out of a network with rational weights
and outputs, linear combinations, thresholds, and multiplicative
connections.  This was a demonstration of the sufficiency of
these elements in combination, not a formal proof of the necessity of
any single element. (But, without multiplicative connections, it
could take an unbounded amount of time to gate rational outputs, which
is necessary to move both ways on the tape in response to threshold
logic; without thresholds, its tough to make a decision; and without
pure linear combinations, its hard not to lose information...)

This is just like the argument that with a couple of registers which
can hold unbounded integers, and the operators Increment, Decrement,
and Branch-on-zero, a stored program machine can universally compute.

I think that other folk, such as Szu and Abu-Mostafa have also worked
on the theoretical two-neuron tape.

Jordan Pollack                            Assistant Professor
CIS Dept/OSU                              Laboratory for AI Research
2036 Neil Ave                             Email: pollack at cis.ohio-state.edu
Columbus, OH 43210                        Fax/Phone: (614) 292-4890

* CS Dept, Univ. of Illinois. Available for $6 as MCCS-87-100 from Librarian/Computing
Research Lab/NMSU/Las Cruces, NM 88003.