English

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}
}
R2 v1 2026-06-28T17:15:51.147Z