In this lecture, we see how to use transducers to produce and recognize outputs.

It is easier to reason about a simpler version of a NFT, one where initial and final states do not have any outputs associated with them, and where each transition outputs either nothing or just a single letter.

While finite state automata seem to suffice in order to describe phonotactic (and morphotactic) well-formedness, phonology (and morphology) actually describes a relation between input and output forms. When we process an output form, we do not (usually) just want to know whether it is well-formed, but rather what inputs it could have arisen from.

What are the languages that can be described by finite automata?

Finite state automata allow us to represent an infinite collection of grammatical forms in a finite way.