Computable one-way functions on the reals
Computational Complexity
2025-07-21 v3 Information Theory
math.IT
Logic
Abstract
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.
Keywords
Cite
@article{arxiv.2406.15817,
title = {Computable one-way functions on the reals},
author = {George Barmpalias and Xiaoyan Zhang},
journal= {arXiv preprint arXiv:2406.15817},
year = {2025}
}