论文标题
在线性非均匀细胞自动机上：二元性和动力学
On linear non-uniform cellular automata: duality and dynamics
论文作者
论文摘要
对于在任意宇宙上的线性非均匀细胞自动机（NUCA），我们介绍并研究了它们的双线性核。概括线性CA的结果，我们表明动态特性，即预注射率，分别。注入性，分别稳定的注射率，分别线性核的可逆性等效于溢流性。解除后，分别稳定的解解率，分别。双线性核的可逆性。但是，虽然Berixtivity是线性CA的双重特性，但线性核不再是这种情况。我们证明，对于线性核，稳定的注射率和稳定的解释后，可以通过左侧的可逆性和右可逆性来精确地表征，并且仅当且仅当它具有前注射性且稳定的后解释时，线性核是可逆的。此外，我们表明线性核满足了重要的阴影特性。还获得了双重表面上的应用。
For linear non-uniform cellular automata (NUCA) over an arbitrary universe, we introduce and investigate their dual linear NUCA. Generalizing results for linear CA, we show that dynamical properties namely pre-injectivity, resp. injectivity, resp. stably injectivity, resp. invertibility of a linear NUCA is equivalent to surjectivity, resp. post-surjectivity, resp. stably post-surjectivity, resp. invertibility of the dual linear NUCA. However, while bijectivity is a dual property for linear CA, it is no longer the case for linear NUCA. We prove that for linear NUCA, stable injectivity and stable post-surjectivity are precisely characterized respectively by left invertibility and right invertibility and that a linear NUCA is invertible if and only if it is pre-injective and stably post-surjective. Moreover, we show that linear NUCA satisfy the important shadowing property. Applications on the dual surjunctivity are also obtained.
