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Turing Computability With Neural Nets (1991)
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| Venue: | Applied Mathematics Letters |
| Citations: | 83 - 15 self |
BibTeX
@ARTICLE{Siegelmann91turingcomputability,
author = {Hava T. Siegelmann and Eduardo D. Sontag},
title = {Turing Computability With Neural Nets},
journal = {Applied Mathematics Letters},
year = {1991},
volume = {4},
pages = {77--80}
}
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Abstract
. This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving processors, interconnected linearly. High-order connections are not required. 1. Introduction This paper addresses the question: What ultimate limitations, if any, are imposed by the use of neural nets as computing devices? In particular, and ignoring issues of training and practicality of implementation, one would like to know if every problem that can be solved by a digital computer is also solvable --in principle-- using a net. This question has been asked before in the literature. Indeed, Jordan Pollack ([7]) showed that a certain recurrent net model --which he called a "neuring machine," for "neural Turing"-- is universal. In his model, all neurons synchronously update their states according to a quadratic combination of past activation values. In general, one calls high-order nets those in...
