论文标题
问题的一阶部分的代数特性
Algebraic properties of the first-order part of a problem
论文作者
论文摘要
在本文中，我们研究了Dzhafarov，Solomon和Yokoyama首次提出的计算问题的一阶部分的概念，该概念捕获了“ Codomain $ \ Mathbb {n} $的“最强大的计算问题，这是weihrauch y Mathbb {n} $可降低为$ f $ $ f $''”。该操作员对于证明分离结果非常有用，尤其是在较高的Weihrauch晶格水平上。我们与文献中已经知道的其他几位运营商有关的一阶部分。我们还介绍了一个新运算符，称为无界有限并行化，该操作员在表征可行问题的一阶部分中起着重要作用。我们展示了如何使用获得的结果来明确表征几个已知问题的一阶部分。
In this paper we study the notion of first-order part of a computational problem, first introduced by Dzhafarov, Solomon, and Yokoyama, which captures the "strongest computational problem with codomain $\mathbb{N}$ that is Weihrauch reducible to $f$". This operator is very useful to prove separation results, especially at the higher levels of the Weihrauch lattice. We explore the first-order part in relation with several other operators already known in the literature. We also introduce a new operator, called unbounded finite parallelization, which plays an important role in characterizing the first-order part of parallelizable problems. We show how the obtained results can be used to explicitly characterize the first-order part of several known problems.
