Results 1  10
of
90
Revisiting the edge of chaos: Evolving cellular automata to perform computations
 Complex Systems
, 1993
"... We present results from an experiment similar to one performed by Packard [24], in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton’s λ parameter [17], and interp ..."
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Cited by 99 (10 self)
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We present results from an experiment similar to one performed by Packard [24], in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton’s λ parameter [17], and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near “critical ” λ values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with λ values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to λ, dynamicalbehavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.
The Evolution of Emergent Computation
, 1995
"... This paper reports the application of new methods for detecting computation in nonlinear processes to a simple evolutionary model that allows us to directly address these questions. The main result is the evolutionary discovery of methods for emergent global computation in a spatially distributed sy ..."
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Cited by 95 (18 self)
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This paper reports the application of new methods for detecting computation in nonlinear processes to a simple evolutionary model that allows us to directly address these questions. The main result is the evolutionary discovery of methods for emergent global computation in a spatially distributed system consisting of locally interacting processors. We use the general term "emergent computation" to describe the appearance of global informationprocessing in such systems (cf. (6,7)). Our goal is to understand the mechanisms by which evolution can discover methods of emergent computation. We are studying this question in a theoretical framework that, while simplified, still captures the essence of the phenomena of interest. This framework requires (i) an idealized class of decentralized system in which global informationprocessing can arise from the actions of simple, locallyconnected units; (ii) a computational task that necessitates global information processing; and (iii) an idealized computational model of evolution. One of the simplest systems in which emergent computation can be studied is a onedimensional binarystate cellular automaton (CA) (8)  a onedimensional spatial lattice of
Computation at the onset of chaos
 The Santa Fe Institute, Westview
, 1988
"... Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubl ..."
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Cited by 83 (14 self)
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Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubling and bandmerging cascades, we derive expressions for the entropy, the interdependence ofmachine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or contextfree Chomsky grammar in this case, we give finite descriptions at the higher computational level of contextfree Lindenmayer systems. We construct a restricted indexed contextfree grammar and its associated oneway nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via
Modelbased Learning for Mobile Robot Navigation from the Dynamical Systems Perspective
 IEEE Transactions on Systems, Man, and Cybernetics
, 1996
"... This paper discusses how a behaviorbased robot can construct a “symbolic process” that accounts for its deliberative thinking processes using models of the environment. The paper focuses on two essential problems; one is the symbol grounding problem and the other is how the internal symbolic proces ..."
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Cited by 80 (20 self)
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This paper discusses how a behaviorbased robot can construct a “symbolic process” that accounts for its deliberative thinking processes using models of the environment. The paper focuses on two essential problems; one is the symbol grounding problem and the other is how the internal symbolic processes can be situated with respect to the behavioral contexts. We investigate these problems by applying a dynamical system’s approach to the robot navigation learning problem. Our formulation, based on a forward modeling scheme using recurrent neural learning, shows that the robot is capable of learning grammatical structure hidden in the geometry of the workspace from the local sensory inputs through its navigational experiences. Furthermore, the robot is capable of generating diverse action plans to reach an arbitrary goal using the acquired forward model which incorporates chaotic dynamics. The essential claim is that the internal symbolic process, being embedded in the attractor, is grounded since it is selforganized solely through interaction with the physical world. It is also shown that structural stability arises in the interaction between the neural dynamics and the environmental dynamics, which accounts for the situatedness of the internal symbolic process. The experimental results using a mobile robot, equipped with a local sensor consisting of a laser range finder, verify our claims. 1 1
The calculi of emergence: Computation, dynamics, and induction
 Physica D
, 1994
"... Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded ..."
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Cited by 77 (14 self)
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Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities. Despite the difficulties, these problems can be analyzed in terms of how modelbuilding observers infer from measurements the computational capabilities embedded in nonlinear processes. An observer’s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference. The discovery of structure in an environment depends more critically and subtlely, though, on how those resources are organized. The descriptive power of the observer’s chosen (or implicit) computational model class, for example, can be an overwhelming determinant in finding regularity in data. This paper presents an overview of an inductive framework — hierarchicalmachine reconstruction — in which the emergence of complexity is associated with the innovation of new computational model classes. Complexity metrics for detecting structure and quantifying emergence, along with an analysis of the constraints on the dynamics of innovation, are outlined. Illustrative examples are drawn from the onset of unpredictability in nonlinear systems, finitary nondeterministic processes, and
Turbulent Pattern Bases for Cellular Automata
 Physica D
, 1993
"... Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the dec ..."
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Cited by 46 (14 self)
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Unpredictable patterns generated by cellular automata (CA) can be decomposed with respect to a turbulent, positive entropy rate pattern basis. The resulting filtered patterns uncover significant structural organization in a CA's dynamics and information processing capabilities. We illustrate the decomposition technique by analyzing a binary, range2 cellular automaton having two invariant chaotic domains of different complexities and entropies. Once identified, the domains are seen to organize the CA's state space and to dominate its evolution. Starting from the domains' structures, we show how to construct a finitestate transducer that performs nonlinear spatial filtering such that the resulting spacetime patterns reveal the domains and the intervening walls and dislocations. To show the statistical consequences of domain detection, we compare the entropy and complexity densities of each domain with the globally averaged quantities. A more graphical comparison uses difference patter...
Computational mechanics: Pattern and prediction, structure and simplicity
 Journal of Statistical Physics
, 1999
"... Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causalstate representation—an Emachine—is the minimal one consistent with ..."
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Cited by 43 (8 self)
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Computational mechanics, an approach to structural complexity, defines a process’s causal states and gives a procedure for finding them. We show that the causalstate representation—an Emachine—is the minimal one consistent with
Computational Mechanics of Cellular Automata: An Example
, 1995
"... We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the spacetime behavior of elementary onedimensional cellular automaton rule 54. The CA's dominant regular domain is identified and a domain filter is constructed to locate and classify d ..."
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Cited by 39 (4 self)
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We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the spacetime behavior of elementary onedimensional cellular automaton rule 54. The CA's dominant regular domain is identified and a domain filter is constructed to locate and classify defects in the domain. The primary particles are identified and a range of interparticle interactions is studied. The deterministic equation of motion of the filtered spacetime behavior is derived. Filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higherlevel defects, particle interactions, and secondary domains. We define the emergence time at which the spacetime behavior condenses into configurations consisting only of domains, particles, and particle interactions. Taken together, these techniques serve as the basis for the investigation of pattern evolution and selforganization in this representative sys...
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 36 (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
Is Anything Ever New? Considering Emergence
 IN
, 1994
"... This brief essay reviews an approach to defining and then detecting the emergence of complexity in nonlinear processes. It is, in fact, a synopsis of Reference [1] that leaves out the technical details in an attempt to clarify the motivations behind the approach. The central puzzle ..."
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Cited by 35 (4 self)
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This brief essay reviews an approach to defining and then detecting the emergence of complexity in nonlinear processes. It is, in fact, a synopsis of Reference [1] that leaves out the technical details in an attempt to clarify the motivations behind the approach. The central puzzle