From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!think.com!linus!linus!elara.mitre.org!escheire Thu Dec 26 23:57:28 EST 1991
Article 2306 of comp.ai.philosophy:
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>From: escheire@elara.mitre.org (Eric Scheirer)
Subject: Re: Turing test, parallel processors, and neural nets
Message-ID: <1991Dec20.135615.14718@linus.mitre.org>
Keywords: Turing test parallel neural nets
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References:  <1991Dec20.061406.1609@news.yale.edu>
Date: Fri, 20 Dec 1991 13:56:15 GMT
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In article <1991Dec20.061406.1609@news.yale.edu>, Peter Seibel writes:
|> How does Turing's proof of the equivalence of all discreet state machines apply
|> to parallel computers and neural nets?  Could they necessarily be simulated on
|> a Universal Turing Machine?  As far as I understand, parallel machines could
|> theoretically be simulated by a UTM, but are there any differences in practice?
|>  (My intuition -- as a non-expert in AI but having thought a lot about it
|> lately -- is that there is some importance difference between actually running
|> several Turing machines in parallel that would be able to access and modify
|> somewhat what is on the other ticker tapes and simulating this on a single
|> machine.  Is there anything to this, and if so is there a more formal way to
|> put it.  Basically my problem is that I can't picture a single tape Turing
|> machine having any sort of self awareness but I can imagine that some sort of
|> massively parallel or neural-net machine might -- but perhaps I am just being a
|> mystic.)
|>  

There is no difference in computing ability between single-head-single-tape, multi-head-
multi-tape, single-head-multi-tape, multi-head-single-tape, etc, etc. Turing machines.  
Actually, there are not, in general, computational differences between a plain-vanilla
Turing machine and one with nearly any simple change you can think of.

To simulate a multi-head multi-tape machine on a single-head-single-tape machine,
just make your tape language for the single-tape machine the cross product of the languages
of the multiple tapes, and similarly for the states of the automaton governing the head motion.

A good reference for these topics (actually, a better text than reference) is Hopcroft & Ullman
(I believe the title is _Introduction to Automata Theory, Languages, and Computation).
------

Eric Scheirer -- Cornell University / The MITRE Corporation
(607) 253-2431 / HORJ@vax5.cit.cornell.edu

There are three kinds of people in the world:
  1. Those who know how many kinds of people there are in the world;
  2. Those who don't.


