Beyond the Existential Theory of the Reals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916640131645440 |
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| author | Schaefer, Marcus Stefankovic, Daniel |
| author_facet | Schaefer, Marcus Stefankovic, Daniel |
| contents | We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness results for various computational problems. We exhibit several families of complete problems which can be used for future completeness results in the real hierarchy. As an application we sharpen some results by Bürgisser and Cucker on the complexity of properties of semialgebraic sets, including the Hausdorff distance problem also studied by Jungeblut, Kleist, and Miltzow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00571 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Beyond the Existential Theory of the Reals Schaefer, Marcus Stefankovic, Daniel Computational Complexity 68Q15, 68Q17, 14P10 We show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness results for various computational problems. We exhibit several families of complete problems which can be used for future completeness results in the real hierarchy. As an application we sharpen some results by Bürgisser and Cucker on the complexity of properties of semialgebraic sets, including the Hausdorff distance problem also studied by Jungeblut, Kleist, and Miltzow. |
| title | Beyond the Existential Theory of the Reals |
| topic | Computational Complexity 68Q15, 68Q17, 14P10 |
| url | https://arxiv.org/abs/2210.00571 |