Computable one-way functions on the reals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912489804922880 |
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| author | Barmpalias, George Zhang, Xiaoyan |
| author_facet | Barmpalias, George Zhang, Xiaoyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computable one-way functions on the reals Barmpalias, George Zhang, Xiaoyan Computational Complexity Information Theory Logic 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. |
| title | Computable one-way functions on the reals |
| topic | Computational Complexity Information Theory Logic |
| url | https://arxiv.org/abs/2406.15817 |