For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are respectively equivalent to nilpotency, periodicity, and eventual periodicity. Moreover, we prove that every linear NUCA which satisfies pointwise a polynomial equation (which may depend on the configuration) must be an eventually periodic linear NUCA. Generalizing results for higher dimensional group and linear CA, we also establish the decidability results of the above dynamical properties as well as the injectivity for arbitrary NUCA with finite memory which are local perturbations of higher dimensional linear and group CA. Some generalizations to the case of sparse global perturbations of higher dimensional linear and group CA are also obtained.
翻译:对于在任意宇宙中具有有限内存且具有多重局部过渡规则的非单式细胞自动成形(中非特派团),我们显示,零度、点周期和点周期性最终周期性分别相当于零度、周期性和最终周期性。此外,我们证明,符合点数多面方程(可能取决于配置)的每一个线性全国团结协会都必须是最终的定期线性 NUCA。 高维组和线性CA的概括性结果,我们还确定了上述动态特性的衰落结果,以及带有有限内存的任意型全国团结协会的投影性,这些内存是高维线和群体CA的局部扰动性。还取得了高维线和群体CA的零星全球扰动情况的一些概括性。