论文标题
非均匀细胞自动机的某些侧重且可决定的特性
Some pointwise and decidable properties of non-uniform cellular automata
论文作者
论文摘要
对于具有有限记忆的非均匀细胞自动气体（NUCA），具有有限的记忆，具有多个局部过渡规则，我们表明，敏捷性，点重周期性和最终周期性特性分别等同于nilpotency，周期性和最终周期性。此外，我们证明，每个线性核心在多项式方程（可能取决于构型）上都必须是最终的周期性线性核。对较高维组和线性CA的概括结果，我们还建立了上述动力学特性的可定性结果，以及具有有限记忆的任意核的注射率，这是有限的局部扰动，这是较高维度线性和组CA的局部扰动。还获得了对较高维度线性和组Ca的稀疏全局扰动的一些概括。
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.
