A major open problem in computational complexity is the existence of a one-way function, namely a function from strings to strings which is computationally easy to compute but hard to invert. Levin (2023) formulated the notion of one-way functions from reals (infinite bit-sequences) to reals in terms of computability, and asked whether partial computable one-way functions exist. We give a strong positive answer using the hardness of the halting problem and exhibiting a total computable one-way function.

翻译：计算复杂性领域的一个主要开放问题是单向函数的存在性，即一种从字符串到字符串的函数，其计算上易于计算但难以求逆。Levin (2023) 从可计算性角度提出了从实数（无限比特序列）到实数的单向函数概念，并探讨了部分可计算单向函数是否存在。我们利用停机问题的困难性给出了一个强烈的肯定答案，并构造了一个完全可计算的单向函数。