In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in ``software'', it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of ``self-organization''. The latter means that the initial configuration does not have to encode an infinite hierarchy -- this will be built up over time. This is a corrected and strengthened version of the journal paper of 2001.

翻译：在概率性元胞自动机中，当所有局部转移均具有正概率时，即使在无限元胞自动机中，无限期保持一个比特信息的问题也非平凡。然而，二维空间存在解决方案，且该方案可用于构造一个简单的三维离散时间通用容错元胞自动机。但该技术对解决以下问题帮助有限：在一维空间中记忆一个比特信息；在低于三维的维度中进行计算；在任意维度中使用非同步转移进行计算。我们提出的更复杂技术将元胞组织成块，这些块对第二个（广义）元胞自动机进行可靠模拟。后者自动机的元胞也组织成块，进而更可靠地模拟第三个自动机，以此类推。由于这一（可能无限）层次结构通过“软件”组织，它必须持续修复由错误引起的损伤。问题的大部分本质上是自稳定过程，即从任意规模和内容的混乱状态中恢复。本文构造了一个异步一维容错元胞自动机，并进一步具备“自组织”特性——所谓自组织，指初始配置无需编码无限层次结构，该结构将在运行过程中逐步构建。本文是2001年期刊论文的修正与强化版本。