The complexity of Boolean functions
The complexity of Boolean functions
On characterizations of the class pspace/poly
Theoretical Computer Science
Sequential simulation of parallel iterations and applications
Theoretical Computer Science
Structural complexity 1
Neurocomputing: foundations of research
Neurocomputing: foundations of research
Simple local search problems that are hard to solve
SIAM Journal on Computing
Efficient simulation of finite automata by neural nets
Journal of the ACM (JACM)
Recursive neural networks for associative memory
Recursive neural networks for associative memory
Circuit complexity and neural networks
Circuit complexity and neural networks
Analog computation via neural networks
Theoretical Computer Science
Computing with truly asynchronous threshold logic networks
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
Computing with continuous-time Liapunov systems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some Afterthoughts on Hopfield Networks
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Continuous-time symmetric Hopfield nets are computationally universal
Neural Computation
On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets
Neural Computation
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We prove that polynomial size discrete 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, i.e., the class computed by polynomial time-bounded nonuniform Turing machines.