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Transducers are automata that have transitions labeled with two symbols. One of the symbols represents input, the other output. Transducers translate (or transduce) strings. In automata theory they are called Mealy machines. Finite state transducers recognize tuples of strings. A set of tuples of strings that can be recognized by an FST is called a regular relation. So, regular relations are to FSTs what regular languages are to FSA.

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