  Given a fixpoint of a substitution, the associated Dumont-Thomas numeration
system provides a convenient immediate way to describe the fixpoint as an
automatic sequence. In order to study first-order properties of these fixpoints
using B\"uchi-Bruy\`ere characterization, it is necessary for the numeration
system to be addable. This means that its addition relation must be computable
by a finite automaton. Dumont-Thomas numeration systems can be regarded as an
extension of positional numeration systems with states where the greediness is
state-dependent. We introduce sequence automata as a tool to extend the results
of Bruy\`ere-Hansel and Frougny-Solomyak on the regularity of the addition of
Bertrand numeration systems to the case of Dumont-Thomas numeration systems
related to some Pisot number. We present a practical implementation of the
addition compatible with the Walnut computation tool, along with some
experimental results.
