具有自组织能力的可靠元胞自动机
Reliable Cellular Automata with Self-Organization
AI总结：
本文提出一种基于块层级、持续修复与自稳定的自组织技术，构造了可从任意初始状态逐步建立无限模拟层级的异步一维容错元胞自动机。
摘要：
在一个所有局部转移都具有正概率的概率元胞自动机中，即使是在无限自动机内，无限期保存一比特信息的问题也并非平凡。尽管如此，二维中仍存在一种解决方案，而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。然而，这项技术对解决以下问题帮助不大：在一维中记忆一比特信息；在低于三维的维度中进行计算；以及在任意维度中使用非同步转移进行计算。我们更复杂的技术将元胞组织成若干块，由这些块对第二个（广义）元胞自动机执行可靠模拟。后一个自动机的元胞也被组织成块，以更高的可靠性模拟第三个自动机，依此类推。由于这一切（可能是无限层级）都以“软件”方式组织，因此必须始终对其进行修复，以消除错误造成的损坏。该问题的很大一部分本质上是自稳定，即从任意规模和任意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，并进一步具有“自组织”特性。后者意味着初始配置不必编码一个无限层级——该层级将随时间逐步建立起来。本文是2001年期刊论文的更正和增强版本。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
