On the Length of Values in a Finite Transducer

The length-degree of a normalized finite transducer (NFT) M is the minimal nonnegative d such that each input word of M only has values with at most d different lengths — or is infinite, depending on whether or not such a d exists. Using the notion of the length-degree, we present some basic results on the lengths of values in a finite transducer. The strongest of these results is: A generalized sequential machine (GSM) with finite length-degree can be effectively decomposed into finitely many GSM's M1,...,MN with length-degree one such that the relation realized by M is the union of the relations realized by M1,...,MN. Using this decomposition, we demonstrate that the equivalence of GSM's with finite length-degree is decidable. By reduction, both results can be easily generalized to NFT's.

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