Although finite state transducers are very natural and simple devices, surprisingly little is known about the transducibility relation they induce on streams (infinite words). We collect some intriguing problems that have been unsolved since several years. The transducibility relation arising from finite state transduction induces a partial order of stream degrees, which we call Transducer degrees , analogous to the well-known Turing degrees or degrees of unsolvability . We show that there are pairs of degrees without supremum and without infimum. The former result is somewhat surprising since every finite set of degrees has a supremum if we strengthen the machine model to Turing machines, but also if we weaken it to Mealy machines.

中文翻译：

---

换能器度数：atoms、infima 和 suprema

尽管有限状态转换器是非常自然和简单的设备，但令人惊讶的是，关于它们在流（无限词）上引起的可转换性关系知之甚少。我们收集了一些多年来一直未解决的有趣问题。由有限状态转导产生的转导关系导致流度的偏序，我们称之为 Transducer degree ，类似于众所周知的图灵度或不可解度。我们证明有没有最高和没有最低的度数对。前一个结果有点令人惊讶，因为如果我们将机器模型增强到图灵机，但如果我们将其弱化到 Mealy 机，那么每个有限度集都有一个上限值。