Analog computation via neural networks
Siegelmann, H.T.
Sontag, E.D.
Rutgers Univ., New Brunswick, NJ;
This paper appears in: Theory and Computing Systems, 1993., Proceedings of the 2nd Israel Symposium on the
Publication Date: 7-9 Jun 1993
On page(s): 98-107
Meeting Date: 06/07/1993 - 06/09/1993
Location: Natanya, Israel
ISBN: 0-8186-3630-0
References Cited: 819
INSPEC Accession Number: 4534572
Digital Object Identifier: 10.1109/ISTCS.1993.253479
Current Version Published: 2002-08-06
Abstract
The authors pursue a particular approach to analog computation,
based on dynamical systems of the type used in neural networks research.
The systems have a fixed structure, invariant in time, corresponding to
an unchanging number of `neurons'. If allowed exponential time for
computation, they turn out to have unbounded power. However, under
polynomial-time constraints there are limits on their capabilities,
though being more powerful than Turing machines. These networks are not
likely to solve polynomially-NP-hard problems, as the equality `P=NP'
implies the almost complete collapse of the standard polynomial
hierarchy. In contrast to classical computational models, the models
studied exhibit at least some robustness with respect to noise and
implementation errors
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