Computable One-Way Functions on the Reals

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.