一句话：引入参数化 Wadge 游戏，刻画 Weihrauch 度的每个下锥，并统一已有多种游戏。
本文研究哪些函数类可由游戏刻画，并给出 Weihrauch 度下锥的统一游戏描述。作者为函数引入参数化的 Wadge 游戏，证明 Weihrauch 度的每个下锥都恰好由这类游戏刻画；该框架涵盖原始 Wadge 游戏、擦除游戏、回溯游戏以及 Semmes 树游戏。作者据此提出，Weihrauch 度的下锥可作为 Andretta 关于函数类游戏刻画问题的答案。文章还讨论若干应用，并利用 Weihrauch 可归约性理论中的机制，通过对可数分支树上的修剪导数进行迭代，给出刻画 Baire 层级每个（超限）层级的游戏。
We introduce a parametrized version of the Wadge game for functions and show that each lower cone in the Weihrauch degrees is characterized by such a game. These parametrized Wadge games subsume the original Wadge game, the eraser and backtrack games as well as Semmes's tree games. In particular, we propose that the lower cones in the Weihrauch degrees are the answer to Andretta's question on which classes of functions admit game characterizations. We then discuss some applications of such parametrized Wadge games. Using machinery from Weihrauch reducibility theory, we introduce games characterizing every (transfinite) level of the Baire hierarchy via an iteration of a pruning derivative on countably branching trees.
@article{paperbot774,
title = {Game characterizations and lower cones in the Weihrauch degrees},
author = {Hugo Nobrega and Arno Pauly},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 3},
year = {2019},
doi = {10.23638/lmcs-15(3:11)2019}
}