Lower Bounds for CSP Hierarchies Through Ideal Reduction

Jonas Conneryd; Yassine Ghannane; Shuo Pang

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arXiv · 2511.17272

Lower Bounds for CSP Hierarchies Through Ideal Reduction

Jonas Conneryd·Yassine Ghannane·Shuo Pang

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Abstract

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].

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BibTeX RIS

Jonas Conneryd, Yassine Ghannane, Shuo Pang. 2025-11-21. Lower Bounds for CSP Hierarchies Through Ideal Reduction. https://arxiv.org/abs/2511.17272

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