  Deterministic two-way transducers on finite words have been shown by
Engelfriet and Hoogeboom to have the same expressive power as
MSO-transductions. We introduce a notion of aperiodicity for these transducers
and we show that aperiodic transducers correspond exactly to FO-transductions.
This lifts to transducers the classical equivalence for languages between
FO-definability, recognition by aperiodic monoids and acceptance by
counter-free automata.
