Weighted finite automata (WFA) define real functions, in particular, grayness functions of graytone images. Inference algorithm that converts an arbitrary function (graytone image) into a WFA that can regenerate it is given in . In this paper we define the theoretical construct of Cooperating Distributed Weighted Finite Automata with n-components (n-WFA) and study the power of this construct in various modes of acceptance. We give an inference algorithm and the de-inference algorithm for the n-WFA. © 2001 Published by Elsevier Science B.V.