Genetic programming, autonomous agents, artif icial life and evolutionary computation share many common ideas. They generally investigate distributed complex processes, perhaps with the ability to interact. It seems to be natural to study their behavior using process algebras, which were designed to handle distributed interactive systems. $-calculus is a higher-order polyadic process algebra for resource bounded computation. It has been designed to handle autonomous agents, evolutionary computing, neural nets, expert systems, machine learning, and distributed interactive AI systems, in general. $-calculus has built-in cost-optimization mechanism allowing to deal with nondeterminism, incomplete and uncertain information. In this paper, we express in $-calculus several subareas of evolutionary computation, including genetic programming, artif icial life, autonomous agents and DNA-based computing. 1

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This paper presents a novel model for resource bounded computation based on process algebras.

Cellular automata (CA) are an abstract model of finegrain parallelism, as the node update operations are rather simple, and therefore comparable to the basic operations of the computer hardware. In a classical CA, all the nodes execute their operations in parallel, that is, (logically) simultaneously. We consider herewith the sequential version of CA, or SCA, and compare it with the classical, parallel CA. In particular, we show that there are 1-D CA with very simple node state update rules that cannot be simulated by any comparable SCA, irrespective of the node update ordering. While the result is trivial if one considers a single computation on a chosen input, we find it both nontrivial, and having some important and far-reaching implications when applied to all possible inputs and, moreover, to the entire nontrivial classes of CA (SCA). We also share some thoughts on how to extend our results herein, and we try motivate the study of genuinely asynchronous cellular automata.

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Abstract. Wegner and Eberbach[Weg04b] have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by so-called superTuring models. In this paper we contest their claims for interaction machines and the πcalculus. 1

A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph classes G, an (F, G)-system is a boolean dynamical system such that all local transition functions lie in F and the underlying graph lies in G. Let F be a class of boolean functions which is closed under composition and let G be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If F contains the self-dual functions and G contains the planar graphs, then the fixed-point existence problem for (F, G)-systems with local transition function given by truth-tables is NP-complete; otherwise, it is decidable in polynomial time. (2) If F contains the self-dual functions and G contains the graphs having vertex covers of size one, then the fixed-point existence problem for (F, G)-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial time. 1

This paper is an attempt to unify classical automata theory and dynamical systems theory. We present a notion of generalized dynamical systems, allowing us to compare properties of both types of systems. Then we etablish a hierachy of dynamical systems, including Turing machines, cellular automata and classical dynamical systems. We finish with some conclusions and motivations for future work. 1 Introduction The theory of finite automata has always been an important field of computer science. Automata, languages, grammars, have been extensively studied [1, 2]. Automata recognize languages and grammars produce languages. Among others, the most studied are finite automata, pushdown automata, Turing machines. The Chomsky hierarchy for languages and grammars is also very well established: regular, context-free, context-sensitive, general grammars generate languages with the same names. The theory of dynamical systems, chaos, attractors [3, 4], is an important field of mathematics and phys...

We study the complexity of image processing and pattern recognition (IPPR) algorithms by their representation as finite cellular automatabased structures. A universal model to represent multilayer homogeneous IPPR algorithms and a technique to compare their quality are required for problems of vision system adaptation, learning, and by the systems for automatic programming. We propose the finite cellular automatabased model for representation of IPPR algorithms and sequential and parallel time complexity measures for this model. Composition and decomposition transformations of proposed structure are suggested and we show that in particular cases they can lead to reduction of complexity. Specific properties of IPPR tasks that are important for their complexity research are discussed.

Connectionist models consist of large numbers of simple but highly interconnected "units". They represent an approach that is quite different from that of classical models based on the structure of Von Neumann machines. Although the term "connectionist models" often refers to artificial neural network models, which are inspired directly by the biological neurons, there are also other connectionist architectures that differ significantly from this biological exemplar. This thesis describes such a "novel" connectionist learning architecture based on the technology of optical thin-film multilayer. The proposed connectionist model consists of multiple thin-film layers (similar to simple processing units in a neural network model), each with different refractive index and thickness. A light beam incident perpendicular to the surface of the multilayer stack is used to carry out the required computation. The reflectance of the light incident can be used as the general measurement of the outputs. Inputs can be fed into the system by encoding them into some system parameters such as refractive indices, and individual layer thicknesses can be used as adjustable parameters that are equivalent to the connection weights of a neural network model. Since this approach involves optical signal processing, the proposed connectionist learning architecture has unique properties and could offer significant advantages. Much of the work has focused on developing this new connectionist learning architecture and investigating its capability to accomplish complex computational tasks which have been extensively studied for conventional connectionist models such as the widely used feed-forward neural network using the back-propagation learning by gradient descent. A prototype simulation model ha...