Inductive Inference of Cellular Automata

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.