Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and parallel algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back to the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., $k$-colourings with $k\neq 3$, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.

翻译：在有限的地方限制下, 我们寻求一个细胞自动图解( 即本地和平行算法), 使满足这些限制的配置实现自我稳定。 更确切地说, 从一个有效配置的有限扰动开始, 细胞自动图解最终必须回到有效配置的空间, 我们允许细胞自动图解使用额外的符号, 但在这种情况下, 额外的符号也可以出现在初始的有限扰动中。 对于一些类型的本地制约( 比如, 美元3元的本地和平行算法), (比如, 美元3元的本地和平行算法), 我们提供高效的自我稳定细胞自动图解, 不管是从一个有效的配置开始, 还是没有额外的符号, 在线性或四面性的时间里, 能够清除有限的扰动。 我们还可以展示一些地方性制约的例子, 自我稳定问题本来就很困难。 我们还会考虑有稳定性的细胞自动图解规则, 并且表明, 在某些情况下, 随机性规则的用途会使问题更加难解。 在开始的初始、 线性配置时, 我们显示, 当一个固定的自我稳定状态下, 当一个固定的自我修正的规律发生于一个固定的固定的固定的固定的固定的固定的固定的固定的固定的固定的规律发生, 。