Edit Distance of Finite-Valued Transducers

TL;DR

This paper proves that the edit distance between finite-valued transducers, which generalize automata by producing multiple outputs, is computable, unlike the uncomputable case for general transducers.

Contribution

It establishes the first known result that the edit distance is computable for finite-valued transducers, a class more expressive than functional transducers.

Findings

Edit distance is computable for finite-valued transducers.

Finite-valued transducers are more expressive than functional transducers.

The work extends the understanding of edit distance computation in automata theory.

Abstract

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.