What is a finite state transducer?

A finite state transducer (FST) is a finite state automaton (FSA, FA) which produces output as well as reading input, which means it is useful for parsing (while a "bare" FSA can only be used for recognizing, i.e. pattern matching).

An FST consists of a finite number of states which are linked by transitions labeled with an input/output pair. The FST starts out in a designated start state and jumps to different states depending on the input, while producing output according to its transition table.

FSTs are useful in NLP and speech recognition because they have nice algebraic properties, most notably that they can be freely combined (form an algebra) under composition, which implements relational composition on regular relations (think of this as non-deterministic function composition) while staying very compact. FSTs can do parsing of regular languages into strings in linear time.

As an example, I once implemented morphological parsing as a bunch of FSTs. My main FST for verbs would turn a regular verb, say "walked", into "walk+PAST". I also had an FST for the verb "to be", which would turn "is" into "be+PRESENT+3rd" (3rd person), and similarly for other irregular verbs. All the FSTs were combined into a single one using an FST compiler, which produced a single FST that was much smaller than the sum of its parts and ran very fast. FSTs can be built by a variety of tools that accept an extended regular expression syntax.

A finite state transducer essentially is a finite state automaton that works on two (or more) tapes. The most common way to think about transducers is as a kind of ``translating machine''. They read from one of the tapes and write onto the other. This, for instance, is a transducer that translates as into bs:

a:b at the arc means that in this transition the transducer reads a from the first tape and writes b onto the second.

Reference: Finite State Transducers