一句话：引入 Cantor 空间上的反馈可计算函数，证明其恰为有效 Borel 函数，并将概念推广到结构上。
本文在反馈图灵计算的基础上，将反馈可计算性从判定问题扩展到 Cantor 空间 2^ω 到 2^ω 的函数，定义反馈可计算函数。关键结果是：这类函数恰好是有效 Borel 函数，从而给出反馈可计算性的精确刻画。受此启发，作者进一步定义一般结构上的反馈可计算函数，不依赖将结构编码为实数，并证明该概念具有绝对性。最后以 Gandy 序数为例，刻画了从带有某有限子集的 Gandy 序数可计算的函数。
We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show that the feedback computable functions are precisely the effectively Borel functions. With this as motivation we define the notion of a feedback computable function on a structure, independent of any coding of the structure as a real. We show that this notion is absolute, and as an example characterize those functions that are computable from a Gandy ordinal with some finite subset distinguished.
@article{paperbot798,
title = {Feedback computability on Cantor space},
author = {Nathanael L. Ackerman and Cameron E. Freer and Robert S. Lubarsky},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 2},
year = {2019},
doi = {10.23638/lmcs-15(2:7)2019}
}