Crutchfield, J. P. (1994), `The calculi of emergence: Computation, dynamics, and induction', Physica D 75, 11--54. Home/Search Document Not in Database Summary Related Articles Check |
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Quantum Automata and Quantum Grammars - Moore, Crutchfield (1 citation) Self-citation (Crutchfield) (Correct)
....context free languages that are not context free. 1 Introduction Nontraditional models of computation such as real valued, analog, spatial, molecular, stochastic, and quantum computation have received a great deal of interest in both physics and computer science in recent years (e.g. [1, 4, 10, 21, 8, 31, 9]) This stems partly from a desire to understand computation in dynamical systems, such as ordinary differential equations, iterated maps, cellular automata, and recurrent neural networks, and partly from a desire to circumvent the fundamental limits on current computingx technologies by inventing ....
.... [24] see also the review in [20] If we generalize the U a to nonlinear maps in R n , we get real time dynamical recognizers [22] If we generalize the U a to nonlinear Bayes optimal update maps of the n simplex, we get ffl machine deterministic representations of recurrent hidden Markov models [8, 36]. Note that the effect of the matrix product Uw = Uw1 Uw2 Delta Delta Delta is to sum over all possible paths that the machine can take. Each path has a complex amplitude equal to the product of the amplitudes of the transitions at each step. Each of Uw s components, representing possible ....
J. P. Crutchfield, "The calculi of emergence: computation, dynamics, and induction." Physica D 75 (1994) 11--54.
Embedded-Particle Computation in Evolved Cellular Automata - Wim Hordijk (1996) (4 citations) Self-citation (Crutchfield) (Correct)
.... and analyzing the intrinsic computational components in the CA s space time behavior in terms of regular domains, particles, and particle interactions [2, 6] This method is part of their computational mechanics framework for understanding information processing embedded in physical systems [1]. Briefly, a regular domain is a homogeneous region of space time in which the same pattern appears. More formally, the spatial patterns in a regular domain can be described by a regular language that is mapped onto itself by the CA rule OE. An embedded particle is a spatially localized, ....
Crutchfield, J. P., "The calculi of emergence: Computation, dynamics, and induction", Physica D 75 (1994), 11--54.
Rule Extraction from Recurrent Neural Networks: A Taxonomy and.. - Jacobsson (2005) (3 citations) (Correct)
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Crutchfield, J. P. (1994), `The calculi of emergence: Computation, dynamics, and induction', Physica D 75, 11--54.
Appendix A Notation - Processes Alphabet (Correct)
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J. P. Crutchfield, "The calculi of emergence: Computation, dynamics, and induction, " Physica D, vol. 75, pp. 11 -- 54, 1994.
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