The Weighted Finite Automaton Inference Problem

Weighted nite automata (WFA) were introduced as a device for generating and transforming pixel images. The inference problem is the determination of a WFA that generates a given image. There are two basic results in this paper. First, a general solution to the inference problem is given which always yields a minimum state WFA for any image. This algorithm uses only addition and inner products of vectors. Second, a connection between the inference problem and basic computational algebraic geometry is established.