Complexity of Linear Equations and Infinite Gadgets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908180472135680 |
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| author | Grebík, Jan Vidnyánszky, Zoltán |
| author_facet | Grebík, Jan Vidnyánszky, Zoltán |
| contents | We investigate the descriptive set-theoretic complexity of the solvability of a Borel family of linear equations over a finite field. Answering a question of Thornton, we show that this problem is already hard, namely $Σ^1_2$-complete. This implies that the split between easy and hard problems is at a different place in the Borel setting than in the case of the CSP Dichotomy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity of Linear Equations and Infinite Gadgets Grebík, Jan Vidnyánszky, Zoltán Logic We investigate the descriptive set-theoretic complexity of the solvability of a Borel family of linear equations over a finite field. Answering a question of Thornton, we show that this problem is already hard, namely $Σ^1_2$-complete. This implies that the split between easy and hard problems is at a different place in the Borel setting than in the case of the CSP Dichotomy. |
| title | Complexity of Linear Equations and Infinite Gadgets |
| topic | Logic |
| url | https://arxiv.org/abs/2501.06114 |