AI 中文总结
本文研究单向和双向元胞自动机（CA）的归纳推理，针对三种不同先验信息的问题变体，提出多项式时间可解且为P完全的推理方法。
AI 中文摘要
本文研究单向和双向元胞自动机（CA）的归纳推理，这涉及推断与有限可用数据兼容的CA。本文中，该信息以有限区间集合的形式提供，每个区间由状态字母表上的两个字w和w'以及一个正整数i组成。目标是推断与每个区间（w,w',i）兼容的CA，即该CA可在i步内从w推导出w'。我们考虑该问题的三种变体：1）CA先验完全已知，目标是验证兼容性；2）CA先验部分已知，目标是将其扩展为兼容的完整CA；3）CA先验完全未知，目标是在存在兼容CA时完全构建它。对于这三种变体，推理均可在多项式时间内完成，且实际上属于P完全问题。
英文摘要
Inductive inference of one- and two-way cellular automata (CA) is considered. This involves inferring a CA that is compatible with a finite amount of available data. In this paper, this information is provided in the form of a finite set of intervals, where each interval consists of two words w and w' over a state set alphabet, with a positive integer i. The goal is to infer a CA which is compatible with each interval (w,w',i), meaning that it can derive w' from w in i steps. We consider three variations of this problem, 1) where the CA is completely known a priori, and the goal is therefore to verify compatibility, 2) where the CA is partially known a priori and the goal is to extend it to a full CA that is compatible, and 3) where the CA is completely unknown, and the goal is to fully construct one that is compatible if one exists. With all three variations, inference can be completed in polynomial time, and is in fact P-complete.
CommentsIn Proceedings AFL 2026, arXiv:2608.23071
Journal refEPTCS 451, 2026, pp. 230-244
