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.

中文翻译：

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无限有序数据字的流变换

在本文中，我们定义了流寄存器转换器 (SRT)，这是一种单向、字母到字母的转导机器模型，用于数据域形成线性群的无限数据字的转换。与现有的数据字转换器相比，SRT 能够对寄存器执行两个额外的操作：基于线性顺序的比较和附加更新。我们考虑可以由 SRT 和 SRT 的几个子类定义的转换。我们调查了这些语言的表达能力和几个决策问题。我们的主要结果包括：1）SRT在并集和交集下是封闭的，无加SRT在组合下也是封闭的；2) SRT 可定义转换可以在 monadic 二阶 (MSO) 逻辑中定义，但不能与一阶 (FO) 可定义转换相比较；