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32
Evolving cellular automata to perform computations: Mechanisms and impediments
 Physica D
, 1994
"... We present results from experiments in which a genetic algorithm (GA) was used to evolve cellular automata (CAs) to perform a particular computational task—onedimensional density classification. We look in detail at the evolutionary mechanisms producing the GA’s behavior on this task and the impedi ..."
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Cited by 113 (16 self)
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We present results from experiments in which a genetic algorithm (GA) was used to evolve cellular automata (CAs) to perform a particular computational task—onedimensional density classification. We look in detail at the evolutionary mechanisms producing the GA’s behavior on this task and the impediments faced by the GA. In particular, we identify four “epochs of innovation ” in which new CA strategies for solving the problem are discovered by the GA, describe how these strategies are implemented in CA rule tables, and identify the GA mechanisms underlying their discovery. The epochs are characterized by a breaking of the task’s symmetries on the part of the GA. The symmetry breaking results in a shortterm fitness gain but ultimately prevents the discovery of the most highly fit strategies. We discuss the extent to which symmetry breaking and other impediments are general phenomena in any GA search. 1.
Classification of Random Boolean Networks
, 2002
"... We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and difference ..."
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Cited by 50 (8 self)
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We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and differences between different types of RBNs with the aid of a public software laboratory we developed. Particularly, we find that the point attractors are independent of the updating scheme, and that RBNs are more different depending on their determinism or nondeterminism rather than depending on their synchronicity or asynchronicity. We also show a way of mapping nonsynchronous deterministic RBNs into synchronous RBNs. Our results are important for justifying the use of specific types of RBNs for modelling natural phenomena.
Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem
 Stanford University
, 1996
"... It is difficult to program cellular automata. This is especially true when the desired computation requires global communication and global integration of information across great distances in the cellular space. Various humanwritten algorithms have appeared in the past two decades for the vexatiou ..."
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Cited by 48 (11 self)
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It is difficult to program cellular automata. This is especially true when the desired computation requires global communication and global integration of information across great distances in the cellular space. Various humanwritten algorithms have appeared in the past two decades for the vexatious majority classification task for onedimensional twostate cellular automata. This paper describes how genetic programming with automatically defined functions evolved a rule for this task with an accuracy of 82.326%. This level of accuracy exceeds that of the original 1978 GacsKurdyumovLevin (GKL) rule, all other known humanwritten rules, and all other known rules produced by automated methods. The rule evolved by genetic programming is qualitatively different from all previous rules in that it employs a larger and more intricate repertoire of domains and particles to represent and communicate information across the cellular space. 1.
Computation in cellular automata: A selected review
 Nonstandard Computation
, 1996
"... 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 o ..."
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Cited by 34 (2 self)
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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
A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications, Ecological Modeling
, 2002
"... and applications ..."
Evolution of intricate longdistance communication signals in cellular automata using genetic programming
 In Artificial Life V: Proceedings of the Fifth International Workshop on the Synthesis and Simulation of Living Systems
, 1996
"... A cellular automata rule for the majority classification task was evolved using genetic programming with automatically defined functions. The genetically evolved rule has an accuracy of 82.326%. This level of accuracy exceeds that of the GacsKurdyumovLevin (GKL) rule, all other known humanwritten ..."
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Cited by 23 (0 self)
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A cellular automata rule for the majority classification task was evolved using genetic programming with automatically defined functions. The genetically evolved rule has an accuracy of 82.326%. This level of accuracy exceeds that of the GacsKurdyumovLevin (GKL) rule, all other known humanwritten rules, and all other rules produced by known previous automated approaches. Our genetically evolved rule is qualitatively different from other rules in that it utilizes a finegrained internal representation of density information; it employs a large number of different domains and particles; and it uses an intricate set of signals for communicating information over large distances in time and space. 1.
Linear Cellular Automata and Fischer Automata
 Parallel Computing
, 1997
"... Introduction Every linear cellular automaton ae can be associated with a regular language L(ae) of finite words: L(ae) is the collection of all finite subwords of configurations that arise after one application of the global map of the cellular automaton. Discussions of the language theoretic aspec ..."
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Cited by 14 (9 self)
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Introduction Every linear cellular automaton ae can be associated with a regular language L(ae) of finite words: L(ae) is the collection of all finite subwords of configurations that arise after one application of the global map of the cellular automaton. Discussions of the language theoretic aspects of linear cellular automata and sofic systems, in particular with respect to their relation to the topology of the space of configurations, can be found in [8], [10] and [7]. In this paper, we will study two measures of complexity associated with L(ae) that are based on minimal finite state machines of a certain type. The first is simply the size of the minimal automaton for L(ae), or, equivalently, the number of left quotients of this language. For the second measure, one can exploit the fact that the languages L(ae) are no
The neglected pillar of material computation
 PHYSICA D
, 2008
"... Many novel forms of computational material have been suggested, from using slime moulds to solve graph searching problems, to using packaging foam to solve differential equations. I argue that attempting to force such novel approaches into the conventional Universal Turing computational framework wi ..."
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Cited by 13 (5 self)
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Many novel forms of computational material have been suggested, from using slime moulds to solve graph searching problems, to using packaging foam to solve differential equations. I argue that attempting to force such novel approaches into the conventional Universal Turing computational framework will provide neither insights into theoretical questions of computation, nor more powerful computational machines. Instead, we should be investigating matter from the perspective of its natural computational capabilities. I also argue that we should investigate nonbiological substrates, since these are less complex in that they have not been tuned by evolution to have their particular properties. Only then we will understand both aspects of computation (logical and physical) required to understand the computation occurring in biological systems.
Updating schemes in random Boolean networks: Do they really matter
 In Artificial Life IX
, 2004
"... In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also ..."
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Cited by 10 (1 self)
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In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the complexity reduction related to different updating schemes. We also report that all updating schemes yield very similar critical stability values, meaning that the “edge of chaos ” does not depend much on the updating scheme. After discussion, we conclude that synchonous RBNs are justifiable theoretical models of biological networks.
Reservoir computing approaches to recurrent neural network training. Comput Sci Rev 2009;3(3):127–49
"... Echo State Networks and Liquid State Machines introduced a new paradigm in artificial recurrent neural network (RNN) training, where an RNN (the reservoir) is generated randomly and only a readout is trained. The paradigm, becoming known as reservoir computing, greatly facilitated the practical app ..."
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Cited by 8 (0 self)
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Echo State Networks and Liquid State Machines introduced a new paradigm in artificial recurrent neural network (RNN) training, where an RNN (the reservoir) is generated randomly and only a readout is trained. The paradigm, becoming known as reservoir computing, greatly facilitated the practical application of RNNs and outperformed classical fully trained RNNs in many tasks. It has lately become a vivid research field with numerous extensions of the basic idea, including reservoir adaptation, thus broadening the initial paradigm to using different methods for training the reservoir and the readout. This review systematically surveys both: current ways of generating/adapting the reservoirs and training different types of readouts. It offers a natural conceptual classification of the techniques, which transcends boundaries of the current “brandnames ” of reservoir methods, and thus aims to help unifying the field and providing the reader with a detailed “map ” of it.