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Cellular automata using infinite computations

机译:使用无限计算的元胞自动机

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This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [10-13]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise metric on the space of definition for one-dimensional cellular automata, whereby accuracy of computations is increased. Using this new metric, open disks are defined and the number of points in each disk is computed. The forward dynamics of a cellular automaton map are also studied via defined equivalence classes. Using the Infinite Unit Axiom, the number of configurations that stay close to a given configuration under the shift automaton map can now be computed.
机译:本文介绍了由Yaroslav Sergeyev(见[10-13])介绍的无限单位公理在一维元胞自动机发展中的应用。此应用程序允许在一维元胞自动机的定义空间上建立新的更精确的度量,从而提高了计算的准确性。使用此新指标,可以定义打开的磁盘并计算每个磁盘中的点数。还通过定义的等价类研究了细胞自动机图的前向动力学。使用无限单位公理,现在可以计算在移位自动机映射下接近给定配置的配置数量。

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