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Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.


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TL;DR: In this paper, the authors present a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations, based on the splitting method which was introduced by the author and which is reminded in the second section of the paper.
Abstract: This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in the second section of the paper. Then we sketchily remind the application to the classical case of the pentagrid, i.e. the tiling of the hyperbolic plane which is generated by reflections of the regular rectangular pentagon in its sides and, recursively, of its images in their sides. From this application, we derived a system of coordinates to locate the tiles, allowing an implementation of cellular automata. At the software level, cells exchange messages thanks to a new representation which improves the speed of contacts between cells. In the new setting, communications are exchanged along actual geodesics and the contribution of the cellular automaton is also linear in the coordinates of the cells.
Proceedings ArticleDOI
01 Jul 2006
TL;DR: A one-dimension cellular automaton traffic flow model, named two-car following model, which can reveal traffic flow's metastable characteristics with better robustness and higher critical density and is completely parallel, so it can adapt to large-scale traffic simulations.
Abstract: A one-dimension cellular automaton traffic flow model, named two-car following model is proposed. Taking into account of the two frontal vehicles' velocity and time-headway when modeling, the model has more traffic information. It can reveal traffic flow's metastable characteristics with better robustness and higher critical density. And the update rule is completely parallel, so it can adapt to large-scale traffic simulations. Theoretical analysis and experimental results reveal that the metastable character is relevant with the relation degree between cars and the random slow probability.
Journal ArticleDOI
TL;DR: It is demonstrated that the channel capacities of the linear automaton and its subautomata can be readily determined by an analytical procedure rather than by applying an iterative algorithm as required for general finite-state automata.
Abstract: A finite-state deterministic linear automaton is viewed as a communication channel from a source to a receiver, accepting source symbols as inputs and generating outputs for a receiver. The automaton is assumed to be composed of two subautomata, one representing the next-state function and one the output function. With the use of Shannon's theorem for capacities of discrete channels, it is demonstrated that the channel capacities of the linear automaton and its subautomata can be readily determined by an analytical procedure rather than by applying an iterative algorithm as required for general finite-state automata.
Journal ArticleDOI
TL;DR: In this paper , the authors consider the problem of self-stabilizing cellular automata under a finite set of local constraints, where the automaton must eventually fall back into the space of valid configurations where it remains still.
Abstract: Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back into the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., $k$-colourings with $k eq 3$, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We note that the optimal self-stabilisation speed is the same for all local constraints that are isomorphic to one another. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.
Journal ArticleDOI
TL;DR: In this article , a coarsened version of one of the standard majority identifiers is presented. But the authors focus on the initial majority identification task and do not consider the complexity of the majority identification problem.
Abstract: The initial majority identification task is a fundamental test problem in cellular automaton research. To pass the test, a two-state automaton has to attain a uniform configuration consisting of only the state that was initially in the majority. It does so solely through its local, internal dynamics—i.e., success in the task is an example of emergent computation. Finding new, better-performing automata continues to be of interest for what additional clues they might reveal about this form of computation. Here we describe a novel, coarsened version of one of the standard majority identifiers. We show that this coarsened system outperforms its parent automaton while significantly reducing the number of computations required to accomplish the task.
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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
202219
20212
20192
20184
201719