@MISC{Litow95theweighted, author = {B. Litow and O. de Vel}, title = {The Weighted Finite Automaton Inference Problem}, year = {1995} }

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Abstract

Weighted finite 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. 1 Introduction Weighted finite automata (WFA) were introduced in [5] as a device for generating and transforming pixel images. WFA have also been used as a means for computing real valued functions [3]. There are several papers reporting a continuing investigation into WFA based image processing, e.g., [4, 6, 2]. As will be seen shortly, WFA are a simple extension of the usual notion of finite automata (FA). This extension is clearest when FA are presented in transition matr...