Abstract:
We investigate the computational power of continuous-time symmetric Hopeld nets. As is well known, such networks have very constrained, Liapunov-function controlled dynamics. Nevertheless, we show that they are universal and ecient computational devices, in the sense that any convergent fully parallel computation by a network of n discrete-time binary neurons, with in general asymmetric interconnections, can be simulated by a symmetric continuous-time Hopeld net containing only 14n + 6 units using the saturated-linear sigmoid activation function. In terms of standard discrete computation models this result implies that any polynomially space-bounded Turing machine can be simulated by a polynomially size-increasing sequence of continuous-time Hopeld nets. 1
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