The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such organisms. We describe a scenario in which an artificial living (AL) system is involved in a potentially infinite, unpredictable interaction with an active or passive environment, to which it can react by learning and adjusting its behaviour. By making use of sequences of cognitive transducers one can also model the evolution of AL systems caused by `architectural' changes. Among the examples are `communities of agents', i.e. by communities of mobile, interactive cognitive transducers.

We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that polynomial-time computations by nondeterministic Turing machines can be reduced to the process of minimizing the energy in Hopfield nets (the MIN ENERGY problem). Furthermore, external and internal sources of energy are distinguished. The external sources include e.g. energizing inputs from so-called Hopfield languages, and also certain external oscillators that prove finite analog Hopfield nets to be computationally Turing universal. On the other hand, the internal source of energy can be implemented by a symmetric clock subnetwork producing an exponential number of oscillations which are used to energize the simulation of convergent asymmetric networks by Hopfield nets. This shows that infinite families of polynomial-size Hopfield nets compute the complexity class PSPACE/poly. A special attention is paid to generalizing these results for analog states and continuous time to point out alternative sources of efficient computation. 1

We survey and summarize the existing literature on the computational aspects of neural network models, by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classi cation include e.g. the architecture of the network (feedforward vs. recurrent), time model (discrete vs. continuous), state type (binary vs. analog), weight constraints (symmetric vs. asymmetric), network size ( nite nets vs. in - nite families), computation type (deterministic vs. probabilistic), etc.

Abstract – This paper presents an observation on adaptation of Hopfield neural network dynamics configured as a relaxation-based search algorithm for static optimization. More specifically, two adaptation rules, one heuristically formulated and the second being gradient descent based, for updating constraint weighting coefficients of Hopfield neural network dynamics are discussed. Application of two adaptation rules for constraint weighting coefficients is shown to lead to an identical form for the update equations. This finding suggests that the heuristically-formulated rule and the gradient descent based rule are analogues of each other. Accordingly, in the current context, common sense reasoning by a domain expert appears to possess a corresponding mathematical framework. 1.

Motivated by applications such as the spread of epidemics and the propagation of influence in social networks, we propose a formal model for analyzing the dynamics of such networks. Our model is a stochastic version of discrete dynamical systems. Using this model, we formulate and study the computational complexity of two fundamental problems (called reachability and predecessor existence problems) which arise in the context of social networks. We also point out the implications of our results on other computational models such as Hopfield networks, communicating finite state machines and systolic arrays. 1

(met een samenvatting in het Nederlands) Proefschrift ter verkrijging van de graad van doctor aan de Universiteit Utrecht op gezag van de Rector Magnificus, Prof. dr. W. H. Gispen, ingevolge het besluit van het College voor Promoties in het openbaar te verdedigen op woensdag 1 februari 2006 des ochtends te 10.30 uur door

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.