元胞自动机在初始测度上迭代后极限测度集的刻画
Characterisation of sets of limit measures after iteration of a cellular automaton on an initial measure
摘要：
在随机构形上迭代的元胞自动机的渐近行为可用其极限概率测度来描述。在本文中，我们的特点措施和措施集，可以达到极限点后，迭代一个简单的初始措施的元胞自动机，在相同的精神SRB措施。除了经典的拓扑约束，我们表现出必要的计算障碍。与一个额外的假设的连接，我们表明这些可计算性条件是足够的，通过构建一个元胞自动机实现这些集，使用辅助状态，以便执行计算。适应这种结构，我们得到了一个类似的表征Cesàro平均收敛，一个赖斯定理的极限点的集合，我们能够执行计算的措施，即细胞自动机收敛到一组极限点，这取决于初始措施。最后，在非满射假设下，可以从构造中删除辅助状态。
英文摘要：
The asymptotic behavior of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after iterating a cellular automaton on a simple initial measure, in the same spirit as SRB measures. In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton realising these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a similar characterization for the Cesàro mean convergence, a Rice theorem on the sets of limit points, and we are able to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from the construction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
