Lower Bounds for CSP Hierarchies Through Ideal Reduction
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915630983151616 |
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| author | Conneryd, Jonas Ghannane, Yassine Pang, Shuo |
| author_facet | Conneryd, Jonas Ghannane, Yassine Pang, Shuo |
| contents | We present a generic way to obtain level lower bounds for (promise) CSP hierarchies from degree lower bounds for algebraic proof systems. More specifically, we show that pseudo-reduction operators in the sense of Alekhnovich and Razborov [Proc. Steklov Inst. Math. 2003] can be used to fool the cohomological $k$-consistency algorithm. As applications, we prove optimal level lower bounds for $c$ vs. $\ell$-coloring for all $\ell \geq c \geq 3$, and give a simplified proof of the lower bounds for lax and null-constraining CSPs of Chan and Ng [STOC 2025]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for CSP Hierarchies Through Ideal Reduction Conneryd, Jonas Ghannane, Yassine Pang, Shuo Computational Complexity 68 F.1.3; F.2.2 We present a generic way to obtain level lower bounds for (promise) CSP hierarchies from degree lower bounds for algebraic proof systems. More specifically, we show that pseudo-reduction operators in the sense of Alekhnovich and Razborov [Proc. Steklov Inst. Math. 2003] can be used to fool the cohomological $k$-consistency algorithm. As applications, we prove optimal level lower bounds for $c$ vs. $\ell$-coloring for all $\ell \geq c \geq 3$, and give a simplified proof of the lower bounds for lax and null-constraining CSPs of Chan and Ng [STOC 2025]. |
| title | Lower Bounds for CSP Hierarchies Through Ideal Reduction |
| topic | Computational Complexity 68 F.1.3; F.2.2 |
| url | https://arxiv.org/abs/2511.17272 |