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Finite-state machines have been used in various domains of natural language processing. We consider here the use of a type of transducer that supports very efficient programs: sequential transducers. We recall classical theorems and give new ones characterizing sequential string-tostring transducers. Transducers that output weights also play an important role in language and speech processing. We give a specific study of string-to-weight transducers, including algorithms for determinizing and minimizing these transducers very efficiently, and characterizations of the transducers admitting determinization and the corresponding algorithms. Some applications of these algorithms in speech recognition are described and illustrated.