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Automata theory is one of the basic theory of computer science , and its broad range of applications . In this paper, a weighted finite state automata (WFA) gray image compression method . Compared with the conventional image coding algorithm , this method has a high compression ratio , the advantages of good compression effect . First of all, the the introductory research background , purpose and significance , as well as domestic and foreign research status and introduced paper involves knowledge , such as linear space , regular languages, finite state machines and other . Second, given the alphabet Σ = { 0 , 1,2,3} language represents the image pixel address given representation of the black-and-white images of finite state automata , and examples of the method in a multi- resolution black and white image , at the same time , given the black-and-white images of finite state automata that algorithm . Finally, the grayscale image compression using weighted finite state automata (WFA) . An input grayscale image , can be represented as a weighted finite state automata . This paper presents two compression algorithms derived algorithm and recursive derivation algorithm has less number of states by the derivation of the algorithm derived WFA , but may have more side ; derivation by the recursive algorithm derived WFA Perhaps the number of states is not the least However , the transition matrix is sparse . The innovation of this paper is that : the introduction of the concept of multi-resolution the average grayscale images stored constant c, the concept of generalized average storage . The average store is a special case of the generalized average storage (c = 1 is the average storage ) . Lt; the c lt ; 1 is the depth of the deepening of the color of the original image , when the c gt ; , depth to the colors of the original image degradation .
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