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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...

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Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper. 1

We present a new self-reproducing cellular automaton capable of construction and computation beyond self-reproduction. Our automaton makes use of some of the concepts developed by Langton for his self-reproducing automaton, but provides the added advantage of being able to perform independent constructional and computational tasks alongside self-reproduction. Our automaton is capable, like Langton's automaton and with comparable complexity, of simple self-replication, but it also provides (at the cost, naturally, of increased complexity) the option of attaching to the automaton an executable program which will be duplicated and executed in each of the copies of the automaton. After describing in some detail the self-reproduction mechanism of our automaton, we provide a non-trivial example of its constructional capabilities. 1 Introduction The history of self-reproducing cellular automata basically begins with John von Neumann's research in the field of complex self-reproducing machi...

We constructed a simple evolutionary system, "evoloop," on a deterministic nine-state five-neighbor cellular automata (CA) space by improving the structurally dissolvable self-reproducing loop we had previously contrived [14] after Langton's self-reproducing loop [7]. The principal role of this improvement is to enhance the adaptability (a degree of the variety of situations in which structures in the CA space can operate regularly) of the self-reproductive mechanism of loops. The experiment with evoloop met with the intriguing result that, though no mechanism was explicitly provided to promote evolution, the loops varied through direct interaction of their phenotypes, smaller individuals were naturally selected thanks to their quicker self-reproductive ability, and the whole population gradually evolved toward the smallest ones. This result gives a unique example of evolution of self-replicators where genotypical variation is caused by precedent phenotypical variation. Such interrelation of genotype and phenotype would be one of the important factors driving the evolutionary process of primitive life forms that might have actually occurred in ancient times.

This article describes in detail an implementation of John von Neumann's self-reproducing machine. Self-reproduction is achieved as a special case of construction by a universal constructor. The theoretical proof of the existence of such machines was given by John von Neumann in the early 1950s [6], but was first implemented in 1994, by the author in collaboration with R. Nobili. Our implementation relies on an extension of the state-transition rule of von Neumann's original cellular automaton. This extension was introduced to simplify the design of the constructor. The main operations in our constructor can be mapped into operations of von Neumann's machine. 1 Introduction Von Neumann [6] introduced constructive universality in cellular automata to study the implementability of self-reproducing machines and to extend the concept of computational universality, introduced by A. Turing [5]. A computing machine is said to be computationally universal if it is capable of simu...

Biological organisms are among the most robust systems known to man. Their robustness is based on a set of processes which cannot be adapted directly to the world of silicon, but can provide an inspiration for the design of robust circuits. This paper introduces a multiplexerbased FPGA which we made capable of self-test and self-repair using an approach loosely based on biological mechanisms at the cellular level. The system is designed to provide on-line self-test and selfrepair using a completely distributed system and a minimal amount of additional logic. 1.

A major impediment of cellular automata (CA) stems from the difficulty of utilizing their complex behavior to perform useful computations. Recent studies by [ Packard, 1988, Mitchell et al., 1994b ] have shown that CAs can be evolved to perform a computational task. In this paper non-uniform CAs are studied, where each cell may contain a different rule, in contrast to the original, uniform model. We describe experiments in which non-uniform CAs are evolved to perform the computational task using a local, co-evolutionary algorithm. For radius r = 3 we attain peak performance values of 0:92 comparable to those obtained for uniform CAs (0:93 \Gamma 0:95). This is notable considering the huge search spaces involved, much larger than the uniform case. Smaller radius CAs (previously unstudied in this context) attain performance values of 0:93 \Gamma 0:94. For r = 1 this is considerably higher than the maximal possible uniform CA performance of 0:83, suggesting that nonuniformity reduces con...

Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior of complex systems in nature. For these reasons CAs and related architectures have