一句话：引入 Weihrauch 复杂度中的无限循环/逆极限算子，证明其单调性并刻画非确定性可计算问题的封闭性。
论文在 Weihrauch 复杂度框架中引入无限循环（逆极限）算子，用以刻画带固定子程序、不断产生结果序列的算法，它对应于无限复合乘积。作者证明该算子对强 Weihrauch 归约单调，但不是闭包算子；并利用递归定理的单射版本与独立选择定理的无穷版本，证明弱 Kőnig 引理在该算子下封闭，从而非确定性可计算问题类也封闭。结果还表明，无限循环算子一般强于菱形算子后接并行化算子，但在许多实际场景中两者一致；文章最后讨论单值问题与 Turing 度上的特殊情形。
We introduce an operator on problems in Weihrauch complexity, which we call the infinite loop or inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a sequence of results in an infinite loop, using some fixed subroutine. We prove that the corresponding operator is monotone with respect to (strong) Weihrauch reducibility but that it is not a closure operator. One of our findings is that weak KÅ‘nig's lemma is closed under infinite loops, which implies that the class of non-deterministically computable problems is also closed under this operation. Consequently, this class allows for a high degree of flexibility in programming. As our main technical tools, we present an injective version of the recursion theorem and an infinitary version of the so-called independent choice theorem. We also show that, in general, the infinite loop operator is more powerful than the composition of the diamond operator followed by the parallelization operator. However, in many practical scenarios, these compositions yield a result, which coincides with the application of the infinite loop operator. Finally, we discuss the special situation of loops for single-valued problems and for problems on Turing degrees.