Transducers generalise automata by producing output word(s) for each input word, thereby defining a relation over words. A transducer is said to be finite-valued if, for every input word, it produces at most $k$ output words, for some constant $k$. If $k = 1$, then the transducer is said to be functional. The edit distance between two transducers is the minimal number of edits required to transform every output of one transducer into some output of the other, for each input word. This notion has been studied for functional transducers, where it is shown to be computable. However, it is uncomputable for transducers in general. In this work, we show the computability of the edit distance of finite-valued transducers, a class that is strictly more expressive than functional transducers.

翻译：转换器通过为每个输入词产生输出词（组），从而定义词上的关系，以此推广了自动机。如果一个转换器对于每个输入词最多产生 $k$ 个输出词（其中 $k$ 为某个常数），则称其为有限值转换器。若 $k = 1$，则称该转换器为功能性转换器。两个转换器之间的编辑距离是指，对于每个输入词，将一个转换器的每个输出转换为另一个转换器的某个输出所需的最少编辑操作次数。这一概念已在功能性转换器中得到研究，并证明其可计算性。然而，对于一般转换器而言，它是不可计算的。在本工作中，我们证明了有限值转换器（一个严格比功能性转换器更具表达力的类别）的编辑距离的可计算性。