Operations on transducers

It is immediately clear that if $\Sigma$ is finite, a pfst defines a regular relation. Therefore, the relations defined by a pfst are closed under various operations such as union, concatenation, Kleene closure and composition. From a practical point of view, it is important to note that it is possible to adapt the constructions for classical transducers for pfst.

The introduction of predicates over symbols is straightforward for operations such as union, concatenation, Kleene closure and cross-product. The identity and composition operations are described now as follows.