  In formal language theory, several different models characterize regular
languages, such as finite automata, congruences of finite index, or monadic
second-order logic (MSO). Moreover, several fragments of MSO have effective
characterizations based on algebraic properties. When we consider transducers
instead of automata, such characterizations are much more challenging, because
many of the properties of regular languages do not generalize to regular word
functions.
  In this paper we consider word functions that are definable by one-way
transducers (rational functions). We show that the canonical bimachine of
Reutenauer and Sch\"utzenberger preserves certain algebraic properties of
rational functions, similar to the case of word languages. In particular, we
give an effective characterization of functions that can be defined by an
aperiodic one-way transducer.
