  In this paper, we define streaming register transducer (SRT), a one-way,
letter-to-letter, transductional machine model for transformations of infinite
data words whose data domain forms a linear group. Comparing with existing data
word transducers, SRT are able to perform two extra operations on the
registers: a linear-order-based comparison and an additive update. We consider
the transformations that can be defined by SRT and several subclasses of SRT.
We investigate the expressiveness of these languages and several decision
problems. Our main results include: 1) SRT are closed under union and
intersection, and add-free SRT are also closed under composition; 2)
SRT-definable transformations can be defined in monadic second-order (MSO)
logic, but are not comparable with first-order (FO) definable transformations;
3) the functionality problem is decidable for add-free SRT, the reactivity
problem and inclusion problem are decidable for deterministic add-free SRT, but
none of these problems is decidable in general for SRT.
