论文标题
伯诺利措施的轨道轨道自动机
Orbits of Bernoulli Measures in Cellular Automata
论文作者
论文摘要
我们讨论了如何在符号的双键空间上构建偏移不变的概率度量，以及如何用块概率来描述此类措施。然后，我们将细胞自动机定义为度量空间中的地图，并讨论这些地图下的偏移不变概率度量的轨道。随后，讨论了局部结构近似值作为在细胞自动机的作用下近似伯努利度量轨道的方法。最终部分提出了一些已知的细胞自动机示例，无论是确定性和概率，对于伯努利度量的轨道元素（短块的概率）可以准确确定。
We discuss how to construct shift-invariant probability measures over the space of bisequences of symbols, and how to describe such measures in terms of block probabilities. We then define cellular automata as maps in the space of measures and discuss orbits of shift-invariant probability measures under these maps. Subsequently, the local structure approximation is discussed as a method to approximate orbits of Bernoulli measures under the action of cellular automata. The final sections presents some known examples of cellular automata, both deterministic and probabilistic, for which elements of the orbit of the Bernoulli measure (probabilities of short blocks) can be determined exactly.
