Continuous-Time Symmetric Hopfield Nets are Computationally Universal

0404612 - UIVT-O 20030009 RIV US eng J - Journal Article
Šíma, Jiří - Orponen, P.
Continuous-Time Symmetric Hopfield Nets are Computationally Universal.
Neural Computation. Roč. 15, č. 3 (2003), s. 693-733. ISSN 0899-7667. E-ISSN 1530-888X
R&D Projects: GA AV ČR IAB2030007; GA ČR GA201/02/1456
Institutional research plan: AV0Z1030915
Keywords : continuous-time Hopfield network * Liapunov function * analog computation * computational power * Turing universality
Subject RIV: BA - General Mathematics
Impact factor: 2.747, year: 2003

We establish a fundamental result in the theory of computation by continuous-time dynamical systems, by showing that systems corresponding to so called continuous-time symmetric Hopfield nets are capable of general computation. As is well known, such networks have very constrained, Liapunov-function controlled dynamics. Nevertheless, we show that they are universal and efficient computational devices, in the sense that any convergent fully parallel computation by a recurrent network of n discrete-time...
Permanent Link: http://hdl.handle.net/11104/0124854