A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric operations
<|reference_start|>A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric operations: 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.<|reference_end|>
@article{zhuk2024a,
    title={A simplified proof of the CSP Dichotomy Conjecture and XY-symmetric
  operations},
    author={Dmitriy Zhuk},
    journal={arXiv preprint arXiv:2404.01080},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.01080},
    primaryClass={cs.CC cs.LO math.RA}
}