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**11 - 12**of**12**### The Computational Theory of Neural Networks

, 2000

"... In the present paper a detailed taxonomy of neural network models with various restrictions is presented with respect to their computational properties. The criteria of classification include e.g. feedforward and recurrent architectures, discrete and continuous time, binary and analog states, symmet ..."

Abstract
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In the present paper a detailed taxonomy of neural network models with various restrictions is presented with respect to their computational properties. The criteria of classification include e.g. feedforward and recurrent architectures, discrete and continuous time, binary and analog states, symmetric and asymmetric weights, finite size and infinite families of networks, deterministic and probabilistic models, etc. The underlying results concerning the computational power of perceptron, RBF, winner-take-all, and spiking neural networks are briey surveyed and completed by relevant references.

### Compressibility of Infinite Binary Sequences

"... It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov comp ..."

Abstract
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It is known that infinite binary sequences of constant Kolmogorov complexity are exactly the recursive ones. Such a kind of statement no longer holds in the presence of resource bounds. Contrary to what intuition might suggest, there are sequences of constant, polynomial-time bounded Kolmogorov complexity that are not polynomial-time computable. This motivates the study of several resource-bounded variants in search for a characterization, similar in spirit, of the polynomial-time computable sequences. We propose some definitions, based on Kobayashi's notion of compressibility, and compare them to both the standard resource-bounded Kolmogorov complexity of infinite strings, and the uniform complexity. Some nontrivial coincidences and disagreements are proved. The resource-unbounded case is also considered. Partially supported by the E.U. through the HCM network CHRX--CT93--0415 (COLORET), by DGICYT, project number PB92--0709, and by the Accion Integrada Hispano-Alemana HA-119-B. 1 ...