Problem
Research questions and friction points this paper is trying to address.
inductive inference
cellular automata
finite data
Inductive Inference of Cellular Automata
🤖 AI Summary
研究通过有限数据推断一维和二维细胞自动机的方法，以验证兼容性、扩展或构建完全未知的细胞自动机，并证明了所有三种情况均可在多项式时间内完成。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
inductive inference
cellular automata
polynomial time
P-completeness
compatibility verification
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