Newsgroups: comp.ai.neural-nets
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From: tsimenne@exeter.ac.uk (T.S.I.Menneer)
Subject: Turing machines and neural nets
Message-ID: <DLBzE6.1np@exeter.ac.uk>
Organization: University of Exeter, UK.
Date: Wed, 17 Jan 1996 15:08:30 GMT
Lines: 36


I am a second-year Ph.D. student researching the hypothesis 
that the use of quantum theory can increase the computational 
power and/or efficiency of neural networks, as it has for 
classical approaches (eg. Shor, Deutsch, Ekert, and others).

Currently, I am trying to establish whether it is accepted 
that neural networks (NNs) are power-equivalent to Turing 
machines (TMs). I have read a number of papers: three by 
Ludermir 1991, Kleene 1956 in Automata Studies, Levelt 1990 
Psych.Res.52, McCulloch and Pitts 1943 Bulletin of Math.
Biophysics.5 and van der Velde 1993 Psych.Res.55. All of these 
papers conclude that real NNs are not equivalent to TMs, rather 
they are finite-state machines. Some of these papers show that 
NNs are equivalent to TMs, given infinite resources. But, the 
definition of a TM is a finite state machine with infinite 
resources, so therefore such proofs are trivial (van der Velde 
1993). However, NN researchers that I have contacted say that NNs 
are power-equivalent to TMs and cite some of these papers. 
This leaves me confused about the relationship between NNs and 
TMs. I would be grateful to hear views on this matter, and of 
any other papers that relate to this topic.

Also, I have been told that there was a discussion a few years 
ago on this newsgroup about quantum theory and NNs. If anyone has 
a record of this discussion, or can remember any conclusions, I 
would be very interested to hear them.

Thank you in advance for your time,
Tammy.

Tamaryn Menneer
Department of Computer Science,	
University of Exeter.
tsimenne@dcs.exeter.ac.uk

