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Computer code written in java is available upon request from the first author.

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Dmitry.Konovalov@jcu.edu.au.

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In this paper, some issues concerning the Chinese remaindering representation are discussed. A new converting method, which is an efficient probabilistic algorithm based on a recent result of von zur Gathen and Shparlinski [J. von zur Gathen, I. Shparlinski, GCD of random linear forms, Algorithmica 46 (2006) 137-148], is described. An efficient refinement of the NC 1 division algorithm of Chiu, Davida and Litow [A. Chiu, G. Davida, B. Litow, Division in logspace-uniform NC 1 , Theoret. Informatics Appl. 35 (2001) 259-275] is given, where the number of moduli is reduced by a factor of log n.

Abstract. We propose and study in details a similarity enrichment scheme for the application to the image compression through the extension of the weighted finite automata (WFA). We then develop a mechanism with which rich families of legitimate similarity images can be systematically created so as to reduce the overall WFA size, leading to an eventual better WFA-based compression performance. A number of desirable properties, including WFA of minimum states, have been established for a class of packed WFA. Moreover, a codec based on a special extended WFA is implemented to exemplify explicitly the performance gain due to extended WFA under otherwise the same conditions.