A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric operations

Dmitriy Zhuk

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arXiv · 2404.01080

A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric operations

Dmitriy Zhuk

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Abstract

We develop a new theory of strong subalgebras and linear congruences that are defined globally. Using this theory we provide a new proof of the correctness of Zhuk's algorithm for all tractable CSPs on a finite domain, and therefore a new simplified proof of the CSP Dichotomy Conjecture. Additionally, using the new theory we prove that composing a weak near-unanimity operation of an odd arity $n$ we can derive an $n$-ary operation that is symmetric on all two-element sets. Thus, CSP over a constraint language $\Gamma$ on a finite domain is tractable if and only if there exist infinitely many polymorphisms of $\Gamma$ that are symmetric on all two-element sets.

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Dmitriy Zhuk. 2024-04-01. A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric operations. https://arxiv.org/abs/2404.01080

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