Computing with continuous-time Liapunov systems

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. More precisely, we prove that any function computed by a discrete-time asymmetric recurrent network of n threshold gates can also be computed by a continuous-time symmetrically-coupled Hopfield system of dimension 18 n +7. Moreover, if the threshold logic network has maximum weight w _{\max} and converges in discrete time t ^*, then the corresponding Hopfield system can be designed to operate in continuous time Θ( t ^*/ε), for any value 0<ε<0.0025 such that w _{\max}2^{3 n }\leq\ε 2^{1/ε}.

Authors

• Jirí Síma
• Pekka Orponen

Keywords

No keywords are indexed for this paper.