## On the Computational Power of Discrete Hopfield Nets (1993)

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Venue: | In: Proc. 20th International Colloquium on Automata, Languages, and Programming |

Citations: | 7 - 4 self |

### BibTeX

@INPROCEEDINGS{Orponen93onthe,

author = {Pekka Orponen},

title = {On the Computational Power of Discrete Hopfield Nets},

booktitle = {In: Proc. 20th International Colloquium on Automata, Languages, and Programming},

year = {1993},

pages = {215--226},

publisher = {Springer-Verlag}

}

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### Abstract

. We prove that polynomial size discrete synchronous Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial space-bounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions P/poly. 1 Background Recurrent, or cyclic, neural networks are an intriguing model of massively parallel computation. In the recent surge of research in neural computation, such networks have been considered mostly from the point of view of two types of applications: pattern classification and associative memory (e.g. [16, 18, 21, 24]), and combinatorial optimization (e.g. [1, 7, 20]). Nevertheless, recurrent networks are capable also of more general types of computation, and issues of what exactly such networks can compute, and how they should be programmed, are becoming increasingly topica...